Can the Schrondinger Wave Equation Be Used to Solve Normalized Cases?

[vick5821]

Homework Statement

Solving Normalized case of schrondinger wave equation

Homework Equations

The Attempt at a Solution

This type of question is not normalized case of solving using schrondiger equation. Any example of solving normalized case using schrondinger equation ? How would it be ? Using same formula and same way of solving ?

Thank you

 

[vela]

The Schrödinger equation is a linear equation, so if $\psi$ is a solution, any constant multiple of it will also be a solution. When normalize the solution, you're simply requiring that the constant be chosen such that
$$\int \psi^*\psi\,dx = 1.$$

 

[vick5821]

Yes. I am aware about that. Just that I wanted some example problem solving on how to solve for normalize case and how would the question asked ?

Thank you

 

[vela]

What do you mean by "solve for normalize case"? I suggest you look up the infinite square well in your textbook. That's probably the simplest example.

 

[vick5821]

As attached, the wave equation given is not normalized case and we solve it using Not Normalized method. I want to ask how would it be if the wave equation given is in NORMALISED form and how to solve it ?

Thank you

 

[vela]

What you're saying doesn't make sense. There is no such thing as a normalized case of the wave equation. You have the wave equation. You find solutions. You normalize the solutions. That's it.

 

[vick5821]

Initially, I get the wave equation , then I try to do see whether the wave equation is normalized or not by see this condition :
If
<refer attachment>

then the wave equation is normalized.

If it is not, means the wave equation is not NORMALIZED

 

[vela]

The (time-independent) wave equation is
$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi + V(x)\psi = E\psi.$$ $\psi$ is a solution to the wave equation.

Take a look at http://physicspages.com/2011/01/26/the-infinite-square-well-particle-in-a-box/.

 

[vick5821]

Have you refer to the very first attachment ? It is given the solution of the wave equation already. But we have to find the momentum in x and y

 

[vick5821]

The (time-independent) wave equation is
$$-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}\psi + V(x)\psi = E\psi.$$ $\psi$ is a solution to the wave equation.



Any similar question ?