A question on Schroedinguer equation

  • Thread starter eljose
  • Start date
  • #1
492
0
let be the SE equation in the form:

[tex]i\bar\frac{d\psi}{dt}=-\frac{\hbar^{2}}{2m}D^{2}\psi+V(x)\psi+NV_{0}\psi [/tex]

where N is a big big number N>>1 then what would be the solution?..thanks.
 

Answers and Replies

  • #2
74
0
That depends on V(x) doesn't it??
 
  • #3
Physics Monkey
Science Advisor
Homework Helper
1,363
34
eljose,

You will find that physical probabilities are independent of [tex] N [/tex] and [tex] V_0 [/tex]. The only thing that will depend on [tex] N V_0 [/tex] is the average total energy. This is a physical consequence of the fact that the reference point of potential energy is arbitrary in quantum mechanics.

This is mathematically evident in that any position independent potential can be absorbed into the wave function as a phase. You can check for yourself that the substitution [tex] \psi = e^{-i N V_0 \,t/\hbar} \psi' [/tex] yields a Schrodinger equation for [tex] \psi' [/tex] given by

[tex]
i \hbar \frac{\partial \psi'}{\partial t} = - \frac{\hbar^2}{2 m} \nabla^2 \psi ' + V(x) \psi'
[/tex]

However, since [tex] \psi [/tex] and [tex] \psi' [/tex] only differ by an overall phase, albeit a time dependent one, they produce the same physics.
 

Related Threads on A question on Schroedinguer equation

  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
3K
Replies
1
Views
568
Replies
12
Views
2K
Replies
2
Views
521
  • Last Post
Replies
16
Views
2K
  • Last Post
Replies
1
Views
772
Replies
3
Views
1K
Top