Searching for beginners' Math for Quantum Physics ( maybe too beginners)

[karkas]

Hello there! I am a new member of Physics Forums, glad to have found you these days!

I am a High School (Lyceum) student in Greece, 16,5 years old and I want to know if there are any books (preferably in pdf form) that I can find and buy, that refer to basic Mathematics about Quantum Physics , that you recommend.

Well I know I am probably very young and some of you would push me to study School stuff, but I am so interested in Advanced Physics and want to delve deep inside this magnificent quantum world. Alas, my Math , being the ones we're taught in school, are SOOO basic that I find everything huge in QP. I myself am putting great effort in learning more and more but still I need help.

So, thanks in advance guys, bring it on!

 

[Hunterbender]

Well, the stanford lectures on quantum entanglement seems ok (well, I am 17 and I can understand most of it). Or you get check out the MIT lectures, but I can't see the board very clearly for MIT (sadly)

both of them are on youtube

 

[MackBlanch]

Quantum Mechanics analysis requires some pretty advanced math. Solving the schrodinger equation requires that you know how to deal with Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs). Then, you will need to have a decent foundation in statistics to understand how to use the solutions you've computed.

However, if you're looking for a more conceptual base, you may just want to find a book and take the math for granted while concentrating on the principles until you can comprehend the math.

 

[confinement]

Before starting to learn QM you should learn the following math subjects in order:

Trigonometry
Introductory Calculus
Linear Algebra
Multivariable Calculus
Differential Equations

You also need to learn some classical physics:

Classical Mechanics
Electromagnetism

 

[j93]

I don't understand all of the threads that are asking for only the math for some section of physics . You need a foundation in related areas of physics like classical mechanics and E & M for Quantum and Quantum/Relativity for QFT. What type of understanding of a physics topic are you expecting with a foundation solely based on math.

 

[MackBlanch]

Many people don't understand that "Physics" is inherently the application of experimentally supported mathematical models. You can get a conceptual understanding of physics based on principles, but you will never be able flush out details without the math.

 

[j93]

Many people don't understand that "Physics" is inherently the application of experimentally supported mathematical models. You can get a conceptual understanding of physics based on principles, but you will never be able flush out details without the math.

Many people do understand that it seems a bigger problem that people don't seem to understand that just because you learn multivariable calc/linear algebra you do not immediately understand E&M or Quantum. Math is part of a toolbox for physicist and just because you own a hammer doesn't mean you know how to build a house
A conceptual understanding of physics is necessary too to understand physics, you can't understand physics based solely on math or at least not in a useful manner. There is nothing as useless as someone who needs to calculate everything because they lack physical intuition.

 

[karkas]

Yes I am studying and probably will study Classical Physics, mechanics, electromagnetism and oscillations for the next two years at least (school level). The fact is that I just want to peak at what's in front of me, since I am hoping to go to a Physics University after I finish school, and since I got myself a basic understanding of Quantum Physics I wanted to proceed to the math. I do know Trigonometry and Basic Math and enough Calculus, it's not that every 16 year old just wants to brag out some math equations and shout "Hey I know String theory, where are the girls and friends!" .

Just like some of you here noticed, I want just to see how a bit more advanced math fits "a bit more advanced" Physics. I understand the fact that I am young and that indeed my Mathematics knowledge can't be richer than a graduate's, but does it hurt so much that I want to learn? Anyway, I know this isn't the proper thread for discussing such a matter, so thanks to everyone who has stayed fixed on the title and helped out. I appreciate it :)

 

[MackBlanch]

Many people do understand that it seems a bigger problem that people don't seem to understand that just because you learn multivariable calc/linear algebra you do not immediately understand E&M or Quantum. Math is part of a toolbox for physicist and just because you own a hammer doesn't mean you know how to build a house
A conceptual understanding of physics is necessary too to understand physics, you can't understand physics based solely on math or at least not in a useful manner. There is nothing as useless as someone who needs to calculate everything because they lack physical intuition.

Fair enough. I have had several math teachers try to use physics as a source of example problem only to see them make a critical conceptual mistake and not be able to identify it because their math was correct.

 

[MackBlanch]

Karkas, your enthusiasm for the topic is admirable. I was griping more than commenting on you as a person. To tailor a response to you, what math are you already familiar and comfortable with?

 

[karkas]

Well, thank you Mack. I am indeed passionate when it comes to Physics these days.

Now, let's see : I am familiar with all the basic math. That is : Equations 1st,2nd grade, what we call in Greek Polyonima (like P(x) , sorry not familiar with the term in English) and their equations, Trigonometry up to cos2x and (cosx)^2 and stuff, trigonometry equations and functions. Furthermore I have a sound knowledge of functions and cartesian applications, when it comes to lines, circles, ellipsoid shapes, parabolas and so on. This means that I can handle difficult situations about basic mathematics.

Now math that I have searched and studied myself, and that I am going to study and be taught in the year to come : Integrals, Derivatives, Logarithms, some (very limited) differential equations.

I really have a rather vast, well as far as you can use such a phrase in my age, knowledge of math. Maybe I should say not at all limited. I think I am in a good road.

I guess that's what you wanted to know, eh?

 

[MackBlanch]

Once you have derivatives and integrals under your belt, you should be prepared to begin looking at QM. I stress 'looking' because you likely will have trouble with the Diff Eq. parts, but it would be good for you to start understanding that QM is a statistical approach and to grow comfortable with that idea. Many people get caught up for a while trying to reconcile themselves with the fact that physics, at what is arguably its most fundamental level, is not deterministic. Einstein, himself, wasn't a fan of this idea ("God doesn't play dice"). I recommend David Griffith's QM book. It offers detailed proofs you may find useful.

 

[gunslingor]

Hey Buddy,

I also would like to say I respect the rare high school student who actually cares about the world, and thus, probably, the way in which it works. I was similar through middle school and high school. I used to buy physics books that were actually way to advanced for my age, but I still learned a lot studying each paragraph over many hours. I decided to become an engineer instead of a Physicist because I felt I could have a greater impact on the world; but physics has always been my passion. I felt that, even if I became a physicist and developed a significant contribution, what good is it if the human race would soon be practically wiped out by, well, climate change or nuclear war. I felt the responsibility to dedicate my life to help ensure this doesn't happen, at least have a small effect on the subject. So that's my life goal now, I work in power. Don't think you are too young, if you want to be a great physicist, start as early as possible. I started ready books on quarks and such when I was 10 (without virtually any math). The point is yes, you should do something, whether it be become great at math or get a good feel for where and why physics is today. You got 2000 years to catch up on, and only 80 years to do it!

Now I am in a similar boat to you. I want to learn the physics in my spare time. I think the logical path is as follows:

basic math
algegra
trig
calculus I, II, III & physics I, II, III
differential equations
quantum theory/mechanics
relativity
special relativity
string theory
superstring theory
M-theory

Consult physics guys to verify. This is the path I intend to follow though I have already completed the first few in college. Quantum theory is where I am currently. Hey Physics guys, Am I on the right path to understanding the universe, at least, as well as some of you might?

I am currently reading "Quantum theory" by David Bohm. I found that it is actually available for free from on Google books here:
http://books.google.com/books?id=9D...m+theory+book&ei=WmCASY2cDKWsNYL0_McE#PPA7,M1

I highly recommend you use Google books for a lot of this. They are on a mission to digitize every out-of-copy-right book every created, to the best of there ability. Things like basic math, algebra, trig calculus I, II, III & physics I, II, III, differential equations haven't changed in 200 years, so any old book would do fine (I still can't get a clear answer from my professors as to why students must purchase a very expensive new edition of algebra books when a 2000 year old Greek versions would probably do fine, lol)

Best of luck

 

[j93]

Three of your book subjects are string theory related I am not sure how far that will get you understanding the universe since the theory is not in the position to be universally accepted and physicist still need to work out details of having that theory make predictions and be completely consistent with any data set people can up with or modified if it does not fit.

 

[ice109]

raise your hand if you actually know any quantum

<raises hand>

Quantum Mechanics analysis requires some pretty advanced math. Solving the schrodinger equation requires that you know how to deal with Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs). Then, you will need to have a decent foundation in statistics to understand how to use the solutions you've computed.

However, if you're looking for a more conceptual base, you may just want to find a book and take the math for granted while concentrating on the principles until you can comprehend the math.

this is all poppy cock. i, knowing odes, pdes, linear algebra, stats, can look back and say that understanding qm doesn't require knowing any of that. e.g. you don't need to know anything about pdes to perform the variable separation that solves the square well problem. you just do it and take for granted that it works. I'm not saying that's how it should be done but that's how it is. no one ever talked to us about uniqueness or existence theorems when they separated the schrondinger eqn; they just did it.

let alone knowing anything real about statistics/probability, again e.g. knowing how to calculate the standard deviation of a data set does not imply knowing any statistics.

note I'm claiming there's a distinction between knowing how to do a variable separation and actually knowing anything about the solution technique.

what i suggest is you find someone who's a decent student, who is taking the class right now, or recently, and willing to show you. personally I'm pretty sure i could explain most of qm to you in 2-3 lectures, depending on what your stamina is like.

 

[MackBlanch]

this is all poppy cock. i, knowing odes, pdes, linear algebra, stats, can look back and say that understanding qm doesn't require knowing any of that. e.g. you don't need to know anything about pdes to perform the variable separation that solves the square well problem. you just do it and take for granted that it works. I'm not saying that's how it should be done but that's how it is. no one ever talked to us about uniqueness or existence theorems when they separated the schrondinger eqn; they just did it.

Stunning. You're being awfully condescending for someone who isn't precise enough to distinguish between conducting analysis and gaining an "understanding". Particularly when any "understanding" you could gain would be highly speculative. Almost every QM book I have used has prefaced itself with a statement asserting that NO ONE really understands QM. Richard Feynman said, "I think I can safely say that nobody understands quantum mechanics." Bohr said, "If you are not confused by quantum physics then you haven't really understood it." David Griffiths wrote, "There is no general consensus as to what its [QM's] fundamental principles are, how it should be taught, or what it really 'means.' Every competent physicist can "do" Quantum Mechanics, but the stories we tell ourselves about what we are doing is as various as the tales of Scheherazade, and almost as implausible."

I stand by what I said. People who want to "do" QM should prepare themselves with the necessary tools. Do you want to be the man using the calculator, or do you want to be the guy who made the calculator?

 

[ice109]

Stunning. You're being awfully condescending for someone who isn't precise enough to distinguish between conducting analysis and gaining an "understanding". Particularly when any "understanding" you could gain would be highly speculative. Almost every QM book I have used has prefaced itself with a statement asserting that NO ONE really understands QM. Richard Feynman said, "I think I can safely say that nobody understands quantum mechanics." Bohr said, "If you are not confused by quantum physics then you haven't really understood it." David Griffiths wrote, "There is no general consensus as to what its [QM's] fundamental principles are, how it should be taught, or what it really 'means.' Every competent physicist can "do" Quantum Mechanics, but the stories we tell ourselves about what we are doing is as various as the tales of Scheherazade, and almost as implausible."

I stand by what I said. People who want to "do" QM should prepare themselves with the necessary tools. Do you want to be the man using the calculator, or do you want to be the guy who made the calculator?

those quotes have absolutely nothing to do with what it means to do quantum mechanics, nor physics; those are statements about empirical science and epistemology in general. again no has ever spoken to me about the interpretation of quantum mechanics, just the prescription.

and about the griffiths quote, i have one, due to him, for you as well in reference to mathematics as a tool: "...it can be tedious and diverting if the instructor feels obliged to give elaborate lessons on the proper use of each tool. My own instinct is to hand the students shovels and tell them to start digging. They may develop blisters at first, but I still think it is the most efficient and exciting way to learn. At any rate, I can assure you that there is no deep mathematics here..."

and I'm being condescending because you're being condescending. what is quantum mechanics analysis? you gain an understanding by doing the problems correctly and interpreting the results. the problems are cheap experiments. they're the next best thing to running all the experiments which is how you truly understand the physics. people like you just make physics, the academic discipline, out to be abstruse when it's not.

and a physicist is a man who only knows "how to use the calculator". even though bardeen made the transistor, very few physicists have contributed to math, computer science, ee, or anything for that matter.

To the OP: get the 3rd edition of griffith's quantum mechanics and get mary boas' math methods book. start reading working/ problems in griffith's. when you get to some math that isn't clear, and there's tons of it because griffith is very sloppy, read boas. if that doesn't help boas has a reference list on everything it covers. hence go get a book that covers only that topic which you are having trouble with.

so here's the prescription:

meet something unintelligible in griffith's like the solution of the harmonic oscillator (fancy words for $x^2$) by hermite polynomials (fancy words for more functions like $x^2$) which isn't clear. go to boas, which is more lucid but might still be insufficient. now go to boyce & diprima for differential equations. if you still can't understand then go ask someone, like a professor at a local college, a physics student, a forum, or even me. don't be shy, there's no shame in asking for help nor will most normal people turn you away. ( for professors though it helps to make appointments via email. )

if you replace all the underlined words with blanks and fill them in every time you have a problem, this prescription will always work and you will be able to learn anything.

 

[udaibothra]

Hello Everyone!

I too am a new member in this forum. I would like to thank Karkas for starting a thread on a topic, I spent the chief of today looking for on the internet, but, without much success.

I too am a 16 year old, and my interests are somewhat similar to Karkas's with an addition of Astrophysics. I, since I was 3 have been interested in Physics, more specifically, the ways of the Universe. As a matter of fact, as a toddler, the pictures in an Isaac Asimov's encyclopedia interested me to such an extent that it played a major part in how I taught myself to read.

All went well till I was 11. I knew about supernova's, dark matter, the bending of light and other such things, you'd find in basic encyclopedias pretty throughly. My enthusiasm was to such an extent that I usually used to get thrown out of class for two reasons primarily- for asking too many questions, or for answering to many, enthusiastically despite repeated warnings from the teacher about not asking out of my turn.

Then, I joined a boarding school.

This is when I saw a catastrophic change in my choice of passions. Owing to a few bad grades in Physics and the general requirement of the school to excel in as many activities you can, I began focusing more and more on sports, music and studies in general.

Though I do not regret the amount I achieved, being an above average student and learning to play the piano along with being a district champion in athletics, I lost touch with the subject, which I today, regard as the most important thing to ever happen to me- The Universe.


I am on student exchange at the moment, and having enough time to do according to my wishes without worrying about the academic pressure, I watched a BBC Documentary about called Atom last week.

Such was its effect that, it has rekindled in me a passion, I'd once lost. I've been watching as many documentaries as I can till today, having just finished one. And I feel that I really want to learn about Physics all again.

Each passing day finds me more and more interested in the subject, but it as a whole but two specific topics of it, or I should say three. Nuclear, Astro and Quantum.

I really don't want to lose this interest again, and for that I want to educate myself as much as I can.

Having gone through the previous posts, I figured one thing out. That you have to have an understanding of Calculus among many other things. For this, I will start with my Calculus tomorrow itself. I am supposed to be taught Calculus this year anyways, but owing to my rocketing interest and the sense of conciousness that I cannot make a further leap into the subjects without a better understanding, I plan to pre-pone my plans a bit.

Can you suggest a book which will come in Handy. A book which I can rely on to educate myself a bit more than my class? Any answers would be very welcome.

I hope you excuse me for this horribly wrong post, but I feel very strongly for the subject and couldn't think of any other way to tell you more about myself.

Any replies would be immensely appreciated.

Thank You! :)

 

[Perspectives]

As a student in the mid 60's, I was studying existentialism and I asked the professor to draw a picture or a diagram that would explain the philosophy. He couldn't do it, despite his understanding of the subject. Mathematics is much the same. It without fanfare or trappings explains something. It without experiment proves the possibility of a thing or process. With all it's eloquence a mathematician will still be at a loss to draw you a picture or verbally explain what is being done to prove a thing. If to operate the symbolics of Mathematics without understanding piece by piece what is happening is mental thumb twilling.

Get someone to draw you a picture or verbally explain what's going on in an equation and you'll be a better Mathematician.

 

[j93]

raise your hand if you actually know any quantum

<raises hand>
this is all poppy cock. i, knowing odes, pdes, linear algebra, stats, can look back and say that understanding qm doesn't require knowing any of that. e.g. you don't need to know anything about pdes to perform the variable separation that solves the square well problem. you just do it and take for granted that it works. I'm not saying that's how it should be done but that's how it is. no one ever talked to us about uniqueness or existence theorems when they separated the schrondinger eqn; they just did it.

let alone knowing anything real about statistics/probability, again e.g. knowing how to calculate the standard deviation of a data set does not imply knowing any statistics.

note I'm claiming there's a distinction between knowing how to do a variable separation and actually knowing anything about the solution technique.

what i suggest is you find someone who's a decent student, who is taking the class right now, or recently, and willing to show you. personally I'm pretty sure i could explain most of qm to you in 2-3 lectures, depending on what your stamina is like.

There is no way you can know quantum without either linear algebra or PDE. Yes you can learn the square well
by taking some things for granted, yes, you can probably learn what is generally regarded as wave mechanics but quantum
mechanics isn't just what you learn at the level of the first few chapters of Griffiths which you could learn without knowing PDEs
or linear algebra. For that matter its possible to learn QM at the level of Griffiths without knowing Linear Algebra or PDE'S but at this level you don't know quantum mechanics, since at this level all you do is plug and chug to equations, you can't derive a thing. At this level your understanding is superficial, as we know all should know physics is not a plug and chug discipline. Memorizing the equation for the Born approximation or second order term in perturbation theory isn't the same as being able to derive it.

How can you learn about wigner-eckart theorem without math or appreciate the relationship between the SU2 group and
angular momentum without math.

 

[j93]

As a student in the mid 60's, I was studying existentialism and I asked the professor to draw a picture or a diagram that would explain the philosophy. He couldn't do it, despite his understanding of the subject. Mathematics is much the same. It without fanfare or trappings explains something. It without experiment proves the possibility of a thing or process. With all it's eloquence a mathematician will still be at a loss to draw you a picture or verbally explain what is being done to prove a thing. If to operate the symbolics of Mathematics without understanding piece by piece what is happening is mental thumb twilling.

Get someone to draw you a picture or verbally explain what's going on in an equation and you'll be a better Mathematician.

To mathematicians defense by drawing something one probably means to give an abstract concept a representation which makes an abstract concept less general and mathematics is about figuring the most general rules.

 

[inempty]

If you have enough time, I think it's a good idea to learn fundamental Calculus and linear algebra initially. It isn't needed to learn them generally and you should just learn the basic methods and concepts, such differential, integral and how to get eigenvalues. Then the best book for you may be the Feynman's lectures. The 3rd volume of it offers a good description of the quantum world, though you may need others' help to read it. It will be perfect if there can be someone teaching you.