# Normalization constant

1. Mar 6, 2005

### sarabellum02

How do I calculate the normalization constant for a wavefunction of the form (r/a)e^(-r/2a) sin(theta)e^(i*phi)?

How would I write the explict harmonic oscillator wavefunction for quantum number 8(in terms on pi, alpha, and y)

thanx

2. Mar 6, 2005

### masudr

Remember that the probability of the particle existing somewhere in all space is certain. So we have

$$\int_{-\infty}^{\infty}\psi\left(x\right)\psi^*\left(x\right)dx=1$$.

For the case of the wavefunction you have been given, an exact anti-derivative exists with these particular limits.

EDIT: Now correct for the 1D case. See jtbell's post for the correct answer.

Last edited: Mar 7, 2005
3. Mar 6, 2005

### Staff: Mentor

No, this is a three-dimensional wave function in spherical coordinates, so the integral looks like this:

$$\int_0^{2 \pi} {\int_0^{\pi} {\int_0^{\infty}{\psi^*(r, \theta, \phi) \psi(r, \theta, \phi)} r^2 \sin \theta \ dr} \ d\theta} \ d\phi} = 1$$

4. Mar 7, 2005

### masudr

Yes, of course, jtbell is correct. Sorry. What I wrote was wrong even in the 1D case.

5. Mar 7, 2005

### dextercioby

It was correct in the ID case,those wave functions are scalars (bosonic variables) and can be switched places inside the integral.

Daniel.

6. Mar 7, 2005

### dextercioby

How many dimensions does this oscillator have...?It's essential to know this fact.As for the variables you posted,they couldn't ring a bell,because notation conventions are not unique...

Daniel.