# Question about Schrödinger equation interpretation

1. Jan 3, 2013

### prehisto

1. The problem statement, all variables and given/known data
Im reading and thinking about the interpretation about Schrödinger equation s solutions (wave functions) - what they realy mean.
What does the amplitude of wave function correspond to?
Does it mean that if amplitude is greater then energy of particle is greater as well ?
I would appreciate any help.
2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 3, 2013

### Simon Bridge

Depends what you mean by "really" ;)
It corresponds to the probability amplitude ... it is it's own thing and does not have a physical meaning by itself. You know that the wave-function, along with it's complex conjugate, form the probability density function for the variable concerned. When you start out you normally have position wave-functions.

So $\psi(x)$ is the solution to Schrodinger's equation in x.
$\psi^\star(x)\psi(x)$ is the probability density function for the particle in x.
$\int_a^b\psi^\star(x)\psi(x) dx$ is the probability of finding the particle with x value between a and b.
Only this last one has a physical meaning ... the rest are steps in a calculation.

No. The amplitude is related to probability. In general, the energy is related to the number of anti-nodes in the wave-function ... in free-space, that would be proportional to the frequency.

3. Jan 4, 2013

### prehisto

Ok,thanks.
Yes, I was thinkinkg whether the amliptude has a physical interpretation.

4. Jan 4, 2013

### Simon Bridge

Only natural.
It is no more physical than the magnitude of a classical probability density.
Technically it is more abstract than that - being a step removed. Some people find it a bit spooky - that such abstract ideas can have a physical impact. You'll find some people almost view the abstract math has having a deeper reality than the stuff you can measure.

Have a look at:
http://vega.org.uk/video/subseries/8
... for a glimpse of how things work.