# What determines an amplitude of a wave particle?

Goodver
According to Bohr's model, photon is emitted when electron "falls" to the lower level with energy equal to the difference between energies on these levels. This determines the frequency of the photon.

What determines an amplitude of a wave created by a single photon, or electron?

Last edited:

Mentor
In general, the amplitude of the wave function is related to the probability of finding the particle at various locations. More specifically the probability density is ##P(x) = |\Psi|^2 = \Psi^*\Psi## where ##\Psi^*## is the complex conjugate of ##\Psi##.

Goodver
Yes, but then how can I find the probability density without knowing an amplitude of the wave function?

I mean, probability density and amplitude depends on each other, so if one side is unknown (amplitude in this case), then the other side also can not be determined

Mentor
Yes, but then how can I find the probability density without knowing an amplitude of the wave function?

You don't. First you find the wave function by solving Schrödinger's equation for the situation that you are interested in, then you use the wave function to find the probability density.

Goodver
deleted

Goodver
Sorry, I am still a bit confused.

by this:

You don't. First you find the wave function by solving Schrödinger's equation for the situation that you are interested in.

You mean I should express ψ(x) from the time independent Schrödinger equation (attached)

substituting values for E, m, h etc (assume I want to calculate amplitude, for defined energy, mass)

?

Then how would I do that? I will always stay with the second derivative of the function and the function itself

Would appreciate if you can give some links on solving Schrödinger equation for this kind of cases

#### Attachments

• CodeCogsEqn (1).gif
1.7 KB · Views: 476
wotanub
Schrodinger's equation is a partial differential equation

Most of the time, it isn't easy (or just impossible) to find an exact solution, but there are about 5 or so instructive problems that are solved exactly in any Quantum mechanics textbook (e.g. Hydrogen atom, harmonic oscillator, etc...).

If you're interested in learning to solve it, I recommend you brush up on your calculus first, then study some quantum mechanics.

Mentor
Many students get their first taste of solving Schrödinger's equation in an "introductory modern physics" course using a textbook such as the ones by Beiser, Tipler, etc.

Almost everyone starts with the "particle in a box" a.k.a. "infinite square well." A Google search should turn up a lot of web pages and university lecture notes.

The version of the SE that you showed is the one for the hydrogen atom. Don't tackle that one until you've done a couple of simpler examples first.