Quantum Physics Reference and Direction

[gunslingor]

Hi,

I am an Electrical and computer engineer. I recently decided to start studying physics in my spare time in the futile attempt to understand the universe, or at least parts and interpretations of it. I decided to start with quantum physics, a book called "Quantum Theory" by David Bohm. It has been good so far. I can even understand a great deal of the math. But the book doesn't really give an introduction to the variables used and just seems to assume the user knows what "J", "k", "a", "del", etc is. I was wondering if someone had a chart, similar to what one might get in a physics II reference chart showing constants and variable symbology, but for quantum physics.

Also, If there are any professors out there, I could use some direction. As an electrical engineer I have had classes in calculus, differential equation, physics I/II, and such to that effect. I could use a road map to understanding; all the way to M-Theory. Any help is appreciated.

 

[DeepThought42]

Hello Gunslinger,

Great book. I recommend you take the free video lectures for Physics 8.03 on the MIT website before you read the book. It will cover much of the math and understanding of waves required. It also follows up on your last Physics II class.

J and K refer to complex coordinates on the complex plane, IE: a + ib where a & b are real numbers

"a" might be confused with a different symbol for the partial derivative. It is the same as a normal derivative "d" except with respect to only one spatial dimension, usually X. It looks like a limp d

del is the gradient, divergence, or curl of the vector. It is sometimes hard to know which is being referred to when that notation is used.

 

[gunslingor]

Hello Gunslinger,

Great book. I recommend you take the free video lectures for Physics 8.03 on the MIT website before you read the book. It will cover much of the math and understanding of waves required. It also follows up on your last Physics II class.

J and K refer to complex coordinates on the complex plane, IE: a + ib where a & b are real numbers

"a" might be confused with a different symbol for the partial derivative. It is the same as a normal derivative "d" except with respect to only one spatial dimension, usually X. It looks like a limp d

del is the gradient, divergence, or curl of the vector. It is sometimes hard to know which is being referred to when that notation is used.

Thanks, I will definitely watch the videos.

I understand the complex plane, but I do not think that is what these variables are intended to represent. If you own the book, look at page 41, section called "action variable". So this variable J, was used a few paragraphs back, and this section is supposed to discuss it. But I have little understand of the significance of this variable. What does a high/low J imply (must be finite value since the integral is over a complete path)?

It took some research since I haven't used the del operator in a while, but I understand most aspects of it. I was hoping the chart I was asking for would list fundamental items such as this. What I need is some sort of 10 pages or less quantum physics chart that shows all variables used in this field of study, showing symbology for each symbol, and perhaps even a description and references for dirivation of equations. Sort of a cheat sheet if you will.

 

[gunslingor]

hey, since you read the same book that I am reading I thought you might be able to help me find a cheet sheet. The book is great, it just doesn't call out what things are. For example, on page 42 there is an equation E=mv^2/2 - Ze^2/r. But it doesn't tell me what the variables are. Usually I would expect to see E=mv^2/2 - Ze^2/r, where Z=blahblah, e=blahblahblah, and v=blahblahblahblah. But there is no WHERE statement! I intuite that m=mass, v=f(in engineering)=frequency, but what is Z and e? I need some kind of a reference so I can read this book. Thanks.

 

[DeepThought42]

J also refers to the density, I will check the book when I get home and confirm.

For example, on page 42 there is an equation E=mv^2/2 - Ze^2/r. But it doesn't tell me what the variables are. Usually I would expect to see E=mv^2/2 - Ze^2/r, where Z=blahblah, e=blahblahblah, and v=blahblahblahblah. But there is no WHERE statement! I intuite that m=mass, v=f(in engineering)=frequency, but what is Z and e? I need some kind of a reference so I can read this book. Thanks.

The first term (positive) is the kinetic energy.

m is mass
v is velocity in meters per second (not to be confused with angular velocity which is rad/s)
*Note: frequency is an italic v

The second term (negative) is the potential energy. Between the electron and the nucleus.

Z is the inverse product of the permittivity of free space and 4pi (Study Maxwell equations if this makes no sense, Physics 8.02)

e is the electric force of the electron and r is the radius or distance from the nucleus.

There are so many different ways to use mathematical symbols and notations that I have had trouble finding one site that covers it all. I have studied each notation on wikipedia and by taking related math classes as I need them.

 

[Jimmy Snyder]

Z is the inverse product of the permittivity of free space and 4pi (Study Maxwell equations if this makes no sense, Physics 8.02).

More likely the equation is the total energy of an electron in the electric field of a nucleus and Z is the number of protons in the nucleus.

 

[DeepThought42]

More likely the equation is the total energy of an electron in the electric field of a nucleus and Z is the number of protons in the nucleus.

If I remember right, it is referencing the hydrogen atom only. The equation would not hold with more than one electron in the system.

 

[Jimmy Snyder]

e is the electric force of the electron ...

More likely e is the electric charge of the electron (and of the proton).

 

[DeepThought42]

More likely e is the electric charge of the electron (and of the proton).

I stand corrected. Ze^2 is the product of the nuclear charge (Ze) and the electron charge (e). For hydrogen Z = 1 and you obtain e^2/r.

I can't see how this equation could work without including the permittivity of free space though. Unless using the natural units. Even then you would still require Ze^2/4pir.

This is because the surface area around the nucleus is proportional to 4pi and the electron is in a stationary state. Some say that the electron is wrapped around the nucleus at all times, even the entire universe at all times. That doesn't work with this classical equation though.

 

[DeepThought42]

J is called the action variable. It is the closed line integral of the momentum taken over the path actually covered by the particle during a single period of oscillation. The single period of oscillation in his text is from one quantum state to the next and back.

The idea is to look into the amount of momentum gained from one oscillation of an electron between 2 states and take the derivative of this with respect to the energy between quantum levels.

There is an explanation on page 41 even though he introduces it before explaining it.

 

[gunslingor]

Thanks for the explanation. I still need some sort of variable symbology and constants reference, i think, in order to really understand this book as it rarely calls out what variables that are being used in equations; probably because the author was trying to provide more of a conceptual understanding than a mathematical understanding, which is great in my opinion, but I still want to understand the details of the math. You mentioned wiki, which page? I have tried searching "action variable" but rarely can find pages like this. Sometimes the book doesn't even give the offical name of the variable, sometimes only a leter is given.

 

[DeepThought42]

The reason the math is not explained is because it is all classical physics mathematics. Taking the online physics lectures will cover most of what you need to know.

If you get stuck on a symbol or meaning here and there, post in the mathematics forums.