Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included? I would like to know the eigenvalues $\omega_i$ for the case of a trapped Bose gas (1D is ok, and for simplicty a step potential can be taken).
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included? I would like to know the eigenvalues $\omega_i$.
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included? I would like to know the eigenvalues $\omega_i$ for the case of a trapped Bose gas (1D is ok, and for simplicty a step potential can be taken).
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included? I would like to know the eigenvalues $\omega_i$.
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included?
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included? I would like to know the eigenvalues $\omega_i$.
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included?
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included?
Can someone please share how you would go on to solve the Bogoliubov-de Gennes equation for a Bose-Einstein condensate with a potential. In particular, how would you deal with the diagonalization when an operator (Laplacian in the Hamiltonian) is included?
