- #1

LCSphysicist

- 646

- 162

- Homework Statement
- All below

- Relevant Equations
- Schrodinger equation in spherical coordinates.

When solving the Schrodinger equation by separation of variables to atom with one electron and in the spherical coordinates, we get $$\Psi = \Theta(\theta)\phi(\varphi)R(r)$$

Specifically, $$\phi = e^{im\rho }$$

The question is, why we adopt this particular solution, in general, we have this options too:

$$\phi = e^{-im\rho } ; sin(m\rho) ; cos(m\rho)$$

I am trying to see what is the problem with the other.

All are univoc, continuous... (actually, we can make it be continuous is better to say!)

Actually, i would say this:

$$cos(m\rho)$$ changes nothing, but is boring deal with.

$$e^{-im\rho }$$ is like to measure the angle clockwise, unnecessary.

$$sin(m\rho)$$ ... nothing too?

Specifically, $$\phi = e^{im\rho }$$

The question is, why we adopt this particular solution, in general, we have this options too:

$$\phi = e^{-im\rho } ; sin(m\rho) ; cos(m\rho)$$

I am trying to see what is the problem with the other.

All are univoc, continuous... (actually, we can make it be continuous is better to say!)

Actually, i would say this:

$$cos(m\rho)$$ changes nothing, but is boring deal with.

$$e^{-im\rho }$$ is like to measure the angle clockwise, unnecessary.

$$sin(m\rho)$$ ... nothing too?