I have to find the eigenfunction of the ground state \Psi_0 of a three independent s=1/2 particle system.
The eigenfunctions \phi_{n,s}(x) = \varphi_n(x) \ \chi_s and eigenvalues E_n of the single particle Hamiltonian are known.
Becuse of the Pauli exclusion principle, there must be...
Hi everyone.
I can not remember if, in 3D, the higher it is the energy level, the higher it is its degeneracy. With a cubic well and with a 3D harmonic oscillator it holds... Does anyone know if it is a general rule or not (and in the case it is, where does this rule come from)?
Hi everyone,
I am working with a solar cell realized with a metal-semiconductor junction. I need to find an expression for the short circuit current of this solar cell, but in the literature I have only found models for the standard case of a pn junction solar cell.
Does anyone know a...
It makes sense, thank you.
Can you just write me down the formula for the energy of a mode of the EM field, containing the two quadratic contributions?
Goodafternoon everyone,
I am looking to the Rayleigh-Jeans law derivation. In order to calculare the average energy of the independent modes of the EM field in the cavity the equipartition of energy is used. In this way, the average energy of a single mode is found to be <E>=kT.
I ask you...
In fact, the text in some parts is not so transparent. Unfortunately, it is the only text that treats so in depth the optical orientation, that is in my domain of interest.
In any case your answer is much clearer.
Thank you!
Of course I can give you the details of the book. The book is: "Optical Orientation", Chapter 7, Section 2.2.
The first part of this chapter is well explained in "Group theory in physics", by Cornwell. Unfortunately the latter book does not discuss the topic of double groups.
If I did write...
I am reading a text about the splitting of the energy levels in crystals caused by the spin orbit interaction. In particular, the argument is treated from the point of view of the group theory.
The text starts saying that a representation (TxD) for the double group can be obtained from the...
S [(1/√2) (|1>|2>-|2>|1>)]=
(1/2)(P12+P21) [(1/√2) (|1>|2>-|2>|1>)] =
(1/2) {[(1/√2) (|1>|2>-|2>|1>)] + [(1/√2) (|2>|1>-|1>|2>)]} =
0
...
At this point, the only thing I can imagine is that
(1/√2) (|1>|2>-|2>|1>)
is an eigenket of S with eigenvalue 0.
Err... right. I did not solve the eigenvalue equation, but I can't see a 4th eigenket of S...
I guess the missing one to form a basis of the ket space is:
(1/√2) (|1>|2>-|2>|1>)
that is an eigenket of A (and thus not of S).
I think in this case the eingevalue is 1 (4 times degenerate), and the eigenkets
|1>|1>
(1/√2) (|1>|2>+|2>|1>)
(1/√2) (|2>|1>+|1>|2>)
|2>|2>
So.. 4 eigenkets for a 4D space. Does this mean that every ket can be obtained as a linear combination of symmetric (antisymmetric) kets?
Hi everyone.
I am studying 'identical particles' in quantum mechanics, and I have a problem with the properties of the Symmetrizer (S) and Antisymmetrizer (A) operators.
S and A are hermitian operators. Therefore, for what I know, their set of eigenkets must constitute a basis of the space...