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4
votes
3answers
2k views

When Eigenfunctions/Wavefunctions are real?

When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real? What happens in 1D case like the finite ...
5
votes
2answers
317 views

If the S-matrix has symmetry group G, must the fields be representations of G?

If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
4
votes
1answer
183 views

Perturbation of an operator - Meaning of matrix element [closed]

Let be $B$ an operator and $\left|\Psi\right>$, $\left|\Phi\right>$ two states (not necessarily equals). What is the meaning of a matrix element $\left<\Psi\right| B ...
2
votes
3answers
475 views

Vector space of $\mathbb{C}^4$ and its basis, the Pauli matrices

How do I write an arbitrary $2\times 2$ matrix as a linear combination of the three Pauli Matrices and the $2\times 2$ unit matrix? Any example for the same might help ?