View Single Post
Tranquillity
#1
Feb27-12, 02:36 PM
P: 15
I have the following Schrodinger equation:

i* (h-bar) * partial derivative of ψ(x,t) w.r.t time
=
[(m*w^2 / 2) * x^2 * ψ(x,t) ] - (1/2m) * (h-bar)^2 * (laplacian of ψ(x,t))]

m>0 is the mass
w is a positive constant

Assume that the ground state (normalizable energy eigenfunction) with the lowest possible energy E(0) is of the form

ψ(x ,t) = A * exp ((-i * E(0)*t/ (h-bar) ) - l * x^2)

A, l are constants

Use the equation to find A and l.


My try:


I know that the Scrodinger eqn can be reduced to a time - independent form which in my case would be


E * ψ (E) = { (-(h-bar)^2 / 2m )* laplacian + (m*w^2 / 2) * x^2} * ψ (E)

Then I am not sure how to proceed.

For the normalization constant I know that the integral from minus infinity to infinity of ψ(x,t)^2 = 1 by Born interpretation for the probability density.

Any help would be greatly appreciated!

Thank you!
Phys.Org News Partner Science news on Phys.org
Wildfires and other burns play bigger role in climate change, professor finds
SR Labs research to expose BadUSB next week in Vegas
New study advances 'DNA revolution,' tells butterflies' evolutionary history