Homework Help: Schroedinger Equation Questions

1. Aug 4, 2011

apigban

Hi! Im having some problems in setting up the Schrodinger equation for a particle described by the wave function:

$\Psi$ = A sinh (x)

should I use the exponential form of the hyperbolic function?

Also, for normalization, do you have any guides that show how to form the complex conjugate of the above function (i dont see the complex parts).

Last edited by a moderator: Apr 26, 2017
2. Aug 4, 2011

Herr Malus

What's the problem with the Schroedinger equation? Are you using the time-independent version (I assume you should be), is there a potential energy associated with this wavefunction?

Further, the complex conjugate of a real valued function is just the real function again. So normalization should look something like:

1=A2 $\int$sinh2(x)dx

Last edited: Aug 4, 2011
3. Aug 4, 2011

apigban

This is my solution to the normalization of the wave equation. Im sorry im totally new at this.

[PLAIN]https://fbcdn-sphotos-a.akamaihd.net/hphotos-ak-snc6/249293_246586558696823_100000364410765_866703_7618168_n.jpg [Broken]

Is it correct? I just followed wikipedia's
http://en.wikipedia.org/wiki/Normalizable_wave_function#Example_of_normalization

My question on the Schroedinger Eq. is that: Should i use the exponential form of the hyperbolic function? or does it matter if i use the hyperbolic? In the normalization above i used the exponential form.

Last edited by a moderator: May 5, 2017
4. Aug 4, 2011

Herr Malus

When you use the wavefunction in the Schrodinger equation, it shouldn't matter what form (hyperbolic or exponential) you use. Your normalization is off however. The integral of sinh2(x) is:

Exponential form: $\frac{1}{4}$ (exp(2x)/2+exp(-2x)/2-2x)
Hyperbolic form: $\frac{1}{4}$ (sinh(2x) -2x)

Further, you need to take the integral only between o and L, the other parts can be ignored. I may be reading this wrong, but it seems like you tried to absorb the exponentials into A2 and ignored any actual integration.

Cheers,
-Malus

5. Aug 4, 2011

apigban

thanks! I did the integration. and found what the factor is. thanks also for pointing that hyperbolic or exponentials can be used!.