A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficie...A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V(x)=x^N. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x)=x^4+iAx are obtained. These zeros exhibit complex version of in terlacing.展开更多
The pseudo Hermiticity with respect to the exchange operators of N-D complexHamiltonians is investigated. It is shown that if an N-D Hamiltonian is pseudo Hermitian and anyeigenfunction of it retains π_αT symmetry t...The pseudo Hermiticity with respect to the exchange operators of N-D complexHamiltonians is investigated. It is shown that if an N-D Hamiltonian is pseudo Hermitian and anyeigenfunction of it retains π_αT symmetry then the corresponding eigen value is real, where π_αis an exchange operator with respect to the permutation a of coordinates and T is the time reversaloperator. We construct a special class of N-D pseudo Hermitian Hamiltonians with respect to exchangeoperators from both N/2-D and N-D general complex Hamiltonians. Examples are presented forHamiltonians with πT symmetry (π : x reversible y, p_x reversible p_y) and the reality of thesesystems are investigated.展开更多
文摘A new semiclassical method is presented for evaluating zeros of wave functions. In this method, locating zeros of the wave functions of Schrodinger equation is converted to finding roots of a polynomial. The coefficients of this polynomial are evaluated using WKB and semi quantum action variable methods. For certain potentials WKB expressions for moments are obtained exactly. Almost explicit formulae for moments are obtained for the potential V(x)=x^N. Examples are given to illustrate both methods. Using semi quantum action variable method, complex zeros of the wave functions of the PT symmetric complex system V(x)=x^4+iAx are obtained. These zeros exhibit complex version of in terlacing.
文摘The pseudo Hermiticity with respect to the exchange operators of N-D complexHamiltonians is investigated. It is shown that if an N-D Hamiltonian is pseudo Hermitian and anyeigenfunction of it retains π_αT symmetry then the corresponding eigen value is real, where π_αis an exchange operator with respect to the permutation a of coordinates and T is the time reversaloperator. We construct a special class of N-D pseudo Hermitian Hamiltonians with respect to exchangeoperators from both N/2-D and N-D general complex Hamiltonians. Examples are presented forHamiltonians with πT symmetry (π : x reversible y, p_x reversible p_y) and the reality of thesesystems are investigated.
