- #1

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- Homework Statement
- How to approach questions with

- Relevant Equations
- $$−ℏ^2/2m d^2ψ(x)/dx2 +U(x)ψx=Eψ(x)$$

Hello folks,

So my level of quantum knowledge is equivalent to what is covered in (year one) two short chapters introducing the topic in Knight's Physics for Scientists and Engineers. Ch. 39 introduces the idea of a wavefunction in a pretty simple way, and ch. 40 touches provides the basics of 1D QM looking at a particle in a box and the essence of infinite square potential wells.

I am looking to apply those basics to the scenario below. The example below comprises an infinitely deep well which is narrow such that in the left hand case, the wave function does not significantly change across its width. I am trying to understand how I would sketch the wave function for the two energy positions Ea and Eb for the right-hand well and work out the Schrodinger equation outside x<0 and x>0, giving the general solution?

I can answer this sort of question for the straightforward case of an infinite square potential well as it's covered in the textbook and there is a lot of good coverage online. But I'm not familiar with how to extend that case to this one? For example, why, if the left-hand case has infinitely deep walls, does the wave function extend beyond the walls?

Are there any accessible resources (first year physics friendly) that will help me with this? Or any explanation that members here might be able to share.

So my level of quantum knowledge is equivalent to what is covered in (year one) two short chapters introducing the topic in Knight's Physics for Scientists and Engineers. Ch. 39 introduces the idea of a wavefunction in a pretty simple way, and ch. 40 touches provides the basics of 1D QM looking at a particle in a box and the essence of infinite square potential wells.

I am looking to apply those basics to the scenario below. The example below comprises an infinitely deep well which is narrow such that in the left hand case, the wave function does not significantly change across its width. I am trying to understand how I would sketch the wave function for the two energy positions Ea and Eb for the right-hand well and work out the Schrodinger equation outside x<0 and x>0, giving the general solution?

I can answer this sort of question for the straightforward case of an infinite square potential well as it's covered in the textbook and there is a lot of good coverage online. But I'm not familiar with how to extend that case to this one? For example, why, if the left-hand case has infinitely deep walls, does the wave function extend beyond the walls?

Are there any accessible resources (first year physics friendly) that will help me with this? Or any explanation that members here might be able to share.