Recent content by jjson775

Your answer is what I was looking for. Thanks. I did take differential equations 60+ years ago but never used it professionally.

Alright. You can’t tell by inspection that the solutions are exponential just because Uo > E is positive, but through solution of the differential equations. I have verified the solutions.

That’s what I said In my post. My reply to PeroK shows my point of confusion. Also, my post has a typo, should have been Uo - E, potential energy > mechanical energy.

I understand that and have checked the solutions. The wording of the text is “Uo - E is positive, so the solutions are exponential functions“. Is this supposed to follow logically? If you drop the word “so”, I am OK.

Between the walls of a finite well, the solution to the time independent Schrodinger equation is a combination of sines and cosines. Outside the walls where E - Uo is positive, the solutions are exponential functions. Why?

Your comment that it can make subsequent math easier is spot on. It showed up in my textbook to show how it satisfies the general wave equation using partial differentiation leading up to introduction of the Schrödinger equation.

Got it. Thanks! I have seen this equation pop up in lectures on YouTube and now in my textbook without any derivation or explanation. A useful mathematical trick, as you say.

I still don’t see where this is headed.

I am a retired engineer, 81 years old, self studying modern physics using Young and Freedman University Physics. I am familiar with the wave equation y(x,t) = A cos (kx - wt) where A = amplitude, k = wave number and w (omega) = angular frequency. in the chapter introducing quantum mechanics...

Correct. I was not used to using the Boltzmann constant in EV.

Thanks. I worked it in Joules and found my arithmetic mistake.

The book I am using for self study is Modern Physics by Serway/Moses/Moyer, 3rd edition. It presumes previous completion of a calculus based physics course, which I have done. I took a series of physics classes as part of an engineering curriculum 60+ years ago that did not include modern...

Got it. Thanks