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

In summary, to write a quantum tunneling equation, you need to be able to solve Schrodinger's equation at the level of a first-year QM class, which requires knowledge of multivariable calculus and differential equations. Additionally, you will need a solid understanding of complex numbers and Euler's formula. However, this will only give you a limited understanding of quantum mechanics, and to fully understand it, you will need to complete an introductory QM course and have a strong background in subjects such as Fourier analysis, complex analysis, and linear algebra. It is not a subject that can be easily learned through popular science texts, and requires a dedicated effort to fully grasp.
  • #1
wolfy
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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
 
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Just to "write a quantum tunneling equation"? You need to be able to solve Schrodinger'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
 
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  • #3
Nugatory said:
Just to "write a quantum tunneling equation"? You need to be able to solve Schrodinger'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.
 
  • #4
wolfy said:
Perhaps a week or 3 should do it.
You might also want to google for "Dunning-Kruger effect"
 
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  • #5
Nugatory said:
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
 
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  • #6
wolfy said:
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.
 
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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.
 
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PeroK said:
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,
 
  • #9
vanhees71 said:
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
 
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  • #10
wolfy said:
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.
 
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  • #11
wolfy said:
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.
 

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

1. What is quantum tunneling?

Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential barrier even though it does not have enough energy to overcome the barrier. This is possible due to the probabilistic nature of quantum mechanics, where a particle can exist in multiple states at the same time.

2. Why is quantum tunneling important?

Quantum tunneling plays a crucial role in many physical processes, such as nuclear fusion in stars, radioactive decay, and the operation of electronic devices like transistors. It also has implications in the development of quantum technologies, such as quantum computing and quantum cryptography.

3. What are the prerequisites for understanding quantum tunneling?

In order to understand quantum tunneling, one should have a solid foundation in quantum mechanics, including concepts such as wave-particle duality, the uncertainty principle, and the Schrödinger equation. Knowledge of basic calculus and linear algebra is also necessary.

4. Can classical mechanics explain quantum tunneling?

No, classical mechanics cannot fully explain quantum tunneling. Classical mechanics is based on the laws of classical physics, which do not apply at the quantum level. Quantum tunneling can only be understood through the principles of quantum mechanics.

5. Are there any real-life applications of quantum tunneling?

Yes, quantum tunneling has several real-life applications, such as in scanning tunneling microscopes, which use quantum tunneling to create images of surfaces at the atomic level. It is also used in the development of tunnel diodes, which have applications in electronic circuits and high-frequency oscillators.

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