why is (psi)n=Asin(npix/L) the energy eigenvalue?
It is definitely not!
What you wrote down is a wavefunction which describes the state of a particle, not an energy, which is ofcourse a number. Also, this is an eigenstate of the Hamiltonian for an infinite square potential well, which you failed to mention that at all. The eigenstates depend on the potential energy function.
So for the infinite square potential well the eigenstates of the Hamiltonian (socalled stationary states) are give by the wavefunction you wrote down. The energy eigenvalue E_n corresponding to psi_n can for example be found by:
[tex]\hat H \psi_n = E_n \psi_n[/tex]
This sgould correspond to the bound state in a square well of length L. The energy inside the (i think) infinite wall shoule be given simply by the second derivative times -hbar^2, hence : the energy eingenvalue should be : En=n^2*pi^2/L^2*hbar^2...
um, i've heard about eigenvalues and eigenfunctions, but this is the first i'm heard about an eigenstate! what's that?
Eigenfunction and eigenstate is the same thing.
In physics we like to refer to the system as being in a 'state' rather than an abstract mathematical entity such as function. Please don't get confused.
thank you very much!!! :)
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