What Prerequisites do I need in order to understand Quantum Tunneling?

[wolfy]

Summary:: What tools like Calculus, Algebra, etc do I need to Understand how to Write a Quantum Tunneling Equation?

I am New to QM however I feel I may have what it takes to do the Math, however, I am not privy to what the Prerequisites are that are needed to perform the Calculations...Calculus, Algebra, Chemistry, Physics, etc...I have a Background in all, however only High School Advanced Final Year...Exactly from a Teacher Perspective what tools do I need in order to get to the Next Level Beyond Basic?

I am a Very Fast Learner as I am Highly Motivated

 

[Nugatory]

Just to "write a quantum tunneling equation"? You need to be able to solve Schrödinger's equation at the level of a first-year QM class. That will require multivariable calculus and multivariable differential equations, stuff that you'll encounter in your second year of calculus (assuming that your first year thoroughly covered single variable differential and integral calculus). You will also have to accept on faith that there is a number $i$ such that $i^2=-1$ and Euler's $e^{i\theta}=\cos\theta+i\sin\theta$.

However... That is a narrow road to a limited and not especially interesting destination - you'll be able to talk about tunnelling in highly idealized and simplified situations, but not much about quantum mechanics. Better would be to do it right and aim for an understanding that comes from completing an intro QM course. For that you will need more math: Fourier analysis, complex analysis, and a solid background in linear algebra. Physics you'll need the full intro courses on classical mechanics at the level of Kleppner and Kolenkow, and E&M at a similar level, and then waves at the level of Crawford. Basically, look for the first two years of a physics BA program

 

[wolfy]

Just to "write a quantum tunneling equation"? You need to be able to solve Schrödinger's equation at the level of a first-year QM class. That will require multivariable calculus and multivariable differential equations, stuff that you'll encounter in your second year of calculus (assuming that your first year thoroughly covered single variable differential and integral calculus). You will also have to accept on faith that there is a number $i$ such that $i^2=-1$ and Euler's $e^{i\theta}=\cos\theta+i\sin\theta$.

However... That is a narrow road to a limited and not especially interesting destination - you'll be able to talk about tunnelling in highly idealized and simplified situations, but not much about quantum mechanics. Better would be to do it right and aim for an understanding that comes from completing an intro QM course. For that you will need more math: Fourier analysis, complex analysis, and a solid background in linear algebra. Physics you'll need the full intro courses on classical mechanics at the level of Kleppner and Kolenkow, and E&M at a similar level, and then waves at the level of Crawford. Basically, look for the first two years of a physics BA program

Thank You for helping me navigate what is needed. These aren't hard things to learn, so shouldn't take to long to get up to speed. Perhaps a week or 3 should do it.

 

[Nugatory]

Perhaps a week or 3 should do it.

You might also want to google for "Dunning-Kruger effect"

 

[wolfy]

You might also want to google for "Dunning-Kruger effect"

The Truth is sometimes funny, you are correct as I spoke too soon.

It would appear that I shall be now spending most of my time in the Calculus Porton of the Forum, for how long I do not know, thanks for grounding my ego

 

[PeroK]

The Truth is sometimes funny, you are correct as I spoke too soon.

It would appear that I shall be now spending most of my time in the Calculus Porton of the Forum, for how long I do not know, thanks for grounding my ego

QM is not that hard to learn, but it's not an elementary subject. There is a difference between popular science texts and the real thing as an academic subject - which requires that you are actualy able to do solve problems yourself.

The most accessible treatment I know can be found here:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

You might want to take a look at that to inspire yourself.

 

[vanhees71]

The difference between a popular-science book and a textbook in quantum mechanics is that you can read through the former quickly and learn at best nothing but most probably something wrong or actively read the latter and learn the right thing. In addition the latter is also much more fun though it takes a lot more work.

 

[wolfy]

QM is not that hard to learn, but it's not an elementary subject. There is a difference between popular science texts and the real thing as an academic subject - which requires that you are actualy able to do solve problems yourself.

The most accessible treatment I know can be found here:

https://physics.mq.edu.au/~jcresser/Phys304/Handouts/QuantumPhysicsNotes.pdf

You might want to take a look at that to inspire yourself.

I am just skimming through it now covers A Lot! Take at least a year to go through it, however, time is not an issue.

Thanks for taking the time PeroK,

 

[wolfy]

The difference between a popular-science book and a textbook in quantum mechanics is that you can read through the former quickly and learn at best nothing but most probably something wrong or actively read the latter and learn the right thing. In addition the latter is also much more fun though it takes a lot more work.

Yes I do not want a laypersons understanding I need the Real Thing no matter how hard or long it takes

 

[kuruman]

Yes I do not want a laypersons understanding I need the Real Thing no matter how hard or long it takes

Here is a video of the great Richard P. Feynman claiming that "nobody understands Quantum Mechanics". Is he joking as evidenced by the audience laughter? After many years of using, almost exclusively, QM in my research, I can claim that I can use it to explain and predict phenomena; I cannot claim that I understand it. I guess that makes me a "shut up and calculate" type of physicist.

 

[PAllen]

I am just skimming through it now covers A Lot! Take at least a year to go through it, however, time is not an issue.

Thanks for taking the time PeroK,

Note, quantum tunneling is introduced in section 5.5.3 of these notes.