quZz
- 123
- 1
Though this question arose in quantum mechanics, i think it should be posted here.
Consider a particle in a well with infinite walls:
[tex] $i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$[/tex]
but the wall start to squeeze
[tex]$\Psi(x=0,t) \equiv 0$[/tex]
[tex]$\Psi(x=a-t,t) = 0$[/tex]
In the beginning the state function is known
[tex]$\Psi(x,t=0) = \varphi(x)[/tex]
What is the method for solving this type of PDE?
Consider a particle in a well with infinite walls:
[tex] $i i \frac{\partial \Psi}{\partial t} = -\frac12 \frac{\partial^2 \Psi}{ \partial x^2},\:0<x<a$[/tex]
but the wall start to squeeze
[tex]$\Psi(x=0,t) \equiv 0$[/tex]
[tex]$\Psi(x=a-t,t) = 0$[/tex]
In the beginning the state function is known
[tex]$\Psi(x,t=0) = \varphi(x)[/tex]
What is the method for solving this type of PDE?