Solving the 3D Schrödinger Equation using Fourier Integral Transform

[sahar1978]

Homework Statement

please if anyone can help me to explain and solve the enclosed equation

 

[CompuChip]

Hi Sahar.

Can you please use the $$\LaTeX$$ capabilities of the forum, or make a screenshot and put it on a site like imageshack?
First of all your attachment is not visible until it is approved, second of all I don't like to open virus-sensitive files like .doc, and finally I don't have M$ Word on my computer.
So if you would switch to one of those options, you can expect much quicker help.

 

[roam]

Here is her question:

How can we solve by using the Fourier integral transform
The 3D Schrödinger equation which given by the form

$$\frac{\partial \psi (x,t)}{\partial t}= \frac{i\eta}{2m} \frac{\partial^2 \psi}{\partial x^2}$$

with the following initial and boundary conditions :

$$\psi (x,0) = \psi_{\circ} (x)$$

$$\psi (x,t) \rightarrow 0$$ as $$\left|x \right| \rightarrow \infty$$, t>0