How Do I Set Up the Schrodinger Equation for This Wave Function?

[apigban]

Hi! I am having some problems in setting up the Schrödinger equation for a particle described by the wave function:

\Psi = A sinh (x)

should I use the exponential form of the hyperbolic function?

[URL]http://62.0.5.135/upload.wikimedia.org/math/9/c/7/9c74b71126c6bb1f4d6b865019a2735e.png[/URL]


Also, for normalization, do you have any guides that show how to form the complex conjugate of the above function (i don't see the complex parts).

 

[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 \intsinh²(x)dx

 

[apigban]

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

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

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.

 

[Herr Malus]

When you use the wavefunction in the Schrödinger 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

 

[apigban]

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