Proving Real & Imaginary Parts of Complex Wavefunction

[Sterj]

A question, If a particle has a wave function like this f(x,t)=e^i(kx-wt) ,is then the probability to find the particle = |f(x,t)|^2?

 

[dextercioby]

No,that's the probability density...It's 1,which means that the wave-function,non square integrable Lebesgue,does not describe a physical state of a quantum system...

Daniel.

 

[Sterj]

that means, if f(x,t) want's to be a wave function |f(x,t)| must be equal to 1. And then the probability density is the integral(ff*dV)

 

[dextercioby]

What?The probability density that the quantum system be found at the moment 't' in the point $\vec{r}$ is $\mathcal{P}=|\Psi(\vec{r},t)|^{2}$ and that's that...

Daniel.

 

[Sterj]

ahh, sure, it has to be so.
A particle can be expressed as a wave, but why the hell it can also be expressed as an oscillator, I mean an oscillator isn't really the same thing as a wave. And why is the ground state energy of a harmonical oscillator the 0-point energy of a particle?
thanks

 

[Raparicio]

Outer product

We have a complex vector space equipped with an inner product, complete with respect to the norm defined by the inner product (i.e. the Hilbert space). Elements of it are vectors. And since it is a complex space, each vector can be multplied by a scalar complex number.
Masud.

Has HIlbert Space an outer product (grassman)? Could it have this?

 

[dextercioby]

Nope,it doesn't.A Hilbert space is what it is.An inner product Banach space.

Daniel.