- #1
pellman
- 684
- 5
Once upon a time I was taking a quantum class and I asked the instructor why we did not cover the linear potential. What happened to F=ma in quantum mechanics? He said it was quite non-trivial and had to be done with Airy functions; not suitable for an introductory class.
Ok.
Given the Schrodinger equation
[tex]\{ -\frac{1}{2m}\frac{\partial^2}{\partial x^2}-Fx\}\Psi=i \frac{\partial\Psi}{\partial t} [/tex]
how about
[tex]\Psi\propto exp\{i[(k+Ft)x-\frac{k^2 t}{2m}-\frac{kFt^2}{2m}-\frac{F^2t^3}{6m}]\}[/tex]
where k is arbitrary?
Why isn't this well known? I spent some time digging through quantum texts in a science library and found only the barest mention of it, just a quick reference in a chapter exercise.
Seems like since it is so very simple it should get mentioned. I presume that it is because it is uninteresting. But why?
Ok.
Given the Schrodinger equation
[tex]\{ -\frac{1}{2m}\frac{\partial^2}{\partial x^2}-Fx\}\Psi=i \frac{\partial\Psi}{\partial t} [/tex]
how about
[tex]\Psi\propto exp\{i[(k+Ft)x-\frac{k^2 t}{2m}-\frac{kFt^2}{2m}-\frac{F^2t^3}{6m}]\}[/tex]
where k is arbitrary?
Why isn't this well known? I spent some time digging through quantum texts in a science library and found only the barest mention of it, just a quick reference in a chapter exercise.
Seems like since it is so very simple it should get mentioned. I presume that it is because it is uninteresting. But why?