Energy levels in quantum well structures

[starla]

Does anyone knows how to solve the following eigenvalue equation using matlab? so as to obtain the energy levels in a quantum well structure.. or does anyone has the codes or knows where to find the codes to do so?

Eigenvalue equation:

tan(sq_root(2mE/hbar^2)*(d/2)) = sq_root((V-E)/E) for even mode (n=2,4,6...)

cot(sq_root(2mE/hbar^2)*(d/2)) = -sq_root((V-E)/E) for odd mode (n=1,3,5...)

where V is the depth of the potential well and m is the effective mass. The eignvalue equation shown above can be numerically solved to yield the energy levels E in a potential well.

 

[George Jones]

Does anyone knows how to solve the following eigenvalue equation using matlab? so as to obtain the energy levels in a quantum well structure.. or does anyone has the codes or knows where to find the codes to do so?

Eigenvalue equation:

tan(sq_root(2mE/hbar^2)*(d/2)) = sq_root((V-E)/E) for even mode (n=2,4,6...)

cot(sq_root(2mE/hbar^2)*(d/2)) = -sq_root((V-E)/E) for odd mode (n=1,3,5...)

where V is the depth of the potential well and m is the effective mass. The eignvalue equation shown above can be numerically solved to yield the energy levels E in a potential well.

Can't you just write, e.g.,

0 = tan(sq_root(2mE/hbar^2)*(d/2)) - sq_root((V-E)/E),

and use the fzero command.