Clear and thorough development of the step potential wave function

[andrewkirk]

I am reading Shankar's "Principles of Quantum Mechanics" and am up to the part where he uses Schrödinger's equation to derive the wave function for various 'simple' scenarios in one spatial dimension.

The first few were fine but his presentation of the step potential problem (specifically, the time evolution of a Gaussian wave packet encountering a step potential) is appalling. It's as though he dashed it off in a hurry one morning when he was late for his train to work. It leaves huge gaps, doesn't explain the steps, uses undefined terms and unintroduced concepts, to the extent that I find parts of it completely impenetrable.

This is a great pity as the step potential problem appears to explain how the amazing phenomenon of quantum tunnelling can occur, and I was really looking forward to understanding that.

Can anybody direct me to a derivation of the wave function for a step potential that is both clear and thorough?

Thank you very much.

 

[dextercioby]

You may check G. Baym's presentation in his <Lectures on Quantum Mechanics>, pp. 88 onwards.

 

[andrewkirk]

Thanks for that recommendation. The lectures appear to only be available by purchasing the book, which would take several weeks as it seems to be hard to get, although Amazon's site says it currently has it. Apparently a few years ago it could only be obtained second-hand.

Would you recommend Baym's text generally as a good introductory text on QM? If so, I'll buy it anyway. I have been wondering about getting one or both of the other texts that are sometimes recommended - Griffiths and Sakurai - but opinions seem sharply divided as to their merits. Maybe Baym is the solution.

Does Baym use bra-ket notation? Having invested in understanding that in the first 100 pages of Shankar, I'd prefer to stick with it if possible.

[What I'd really like to buy is the boxed set of Feynman's lectures, but Amazon won't sell them to anybody outside the USA.]

Thanks again