The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies...The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies a canonical transformation. Using the to describe the system, it is proved that if the Hartrec type approximation is adopted, or the c-number approach is used, the Bogoliubov transformation can be derived via the U-matrix theory if the perturbing Hamiltonian is turned on ’suddenly’. It is also shown that based on the U-matrix, the BCS ground state wave function of a superconducting system can be deduced under the sudden switching condition.展开更多
The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equati...The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.展开更多
文摘The U-matrlx theory in quantum mechanics recently developed has been appliedto study a superconductor system described by the BCS pairing Hamiltonian . It is shown that in general the -operator in our theory specifies a canonical transformation. Using the to describe the system, it is proved that if the Hartrec type approximation is adopted, or the c-number approach is used, the Bogoliubov transformation can be derived via the U-matrix theory if the perturbing Hamiltonian is turned on ’suddenly’. It is also shown that based on the U-matrix, the BCS ground state wave function of a superconducting system can be deduced under the sudden switching condition.
文摘The 'trial function method' ( TFM for short) and a routine way in finding traveling,wave solutions to some nonlinear partial differential equations( PDE for short), wer explained. Two types of evolution equations are studied, one is a generalized Burgers or KdV equation, the other is the Fisher equation with special nonlinear forms of its reaction rate term. One can see that this method is simple, fast and allowing further extension.
