Analytic Expression for Exact Ground State Energy Based on an Operator Method for a Class of Anharmonic Potentials

A general procedure based on shift operators is formulated to deal with anharmonic potentials. It is possible to extract the ground state energy analytically using our method provided certain consistency relations are satisfied. Analytic expressions for the exact ground state energy have also been derived specifically for a large class of the one-dimensional oscillator with cubic-quartic anharmonic terms. Our analytical results can be used to check the accuracy of existing numerical methods, for instance the method of state-dependent diagonalization. Our results also agree with the asymptotic behavior in the divergent pertubative expansion of quartic harmonic oscillator.Comment: LaTeX with six figure (gif) files; Submitted to Phys. Rev.

A unified approach for exactly solvable potentials in quantum mechanics using shift operators

We present a unified approach for solving and classifying exactly solvable potentials. Our unified approach encompasses many well-known exactly solvable potentials. Moreover, the new approach can be used to search systematically for a new class of solvable potentials.Comment: RevTex, 8 page

General Approach to Functional Forms for the Exponential Quadratic Operators in Coordinate-Momentum Space

In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061; quant-ph/9605032], the one dimensional squeezed and harmonic oscillator time-displacement operators were reordered in coordinate-momentum space. In this paper, we give a general approach for reordering multi-dimensional exponential quadratic operator(EQO) in coordinate-momentum space. An explicit computational formula is provided and applied to the single mode and double-mode EQO through the squeezed operator and the time displacement operator of the harmonic oscillator.Comment: To appear in J. Phys. A: Mathematics and Genera

On Bures fidelity of displaced squeezed thermal states

Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this paper, we give a formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters and birefly discuss how the results can apply to quantum information theory.Comment: 10 pages with RevTex require

Persistent Current From the Competition Between Zeeman Coupling and Spin-Orbit Interaction

Applying the non-adiabatic Aharonov-Anandan phase approach to a mesoscopic ring with non-interacting many electrons in the presence of the spin-orbit interaction, Zeeman coupling and magnetic flux, we show that the time-reversal symmetry breaking due to Zeeman coupling is intrinsically different from that due to magnetic flux. We find that the direction of the persistent currents induced by the Zeeman coupling changes periodically with the particle number, while the magnetic flux determines the direction of the induced currents by its sign alone.Comment: 5 pages, ReVTeX, including 3 figures on request,Submitted to Phys.Rev.Let

Spin Precession and Time-Reversal Symmetry Breaking in Quantum Transport of Electrons Through Mesoscopic Rings

We consider the motion of electrons through a mesoscopic ring in the presence of spin-orbit interaction, Zeeman coupling, and magnetic flux. The coupling between the spin and the orbital degrees of freedom results in the geometric and the dynamical phases associated with a cyclic evolution of spin state. Using a non-adiabatic Aharonov-Anandan phase approach, we obtain the exact solution of the system and identify the geometric and the dynamical phases for the energy eigenstates. Spin precession of electrons encircling the ring can lead to various interference phenomena such as oscillating persistent current and conductance. We investigate the transport properties of the ring connected to current leads to explore the roles of the time-reversal symmetry and its breaking therein with the spin degree of freedom being fully taken into account. We derive an exact expression for the transmission probability through the ring. We point out that the time-reversal symmetry breaking due to Zeeman coupling can totally invalidate the picture that spin precession results in effective, spin-dependent Aharonov-Bohm flux for interfering electrons. Actually, such a picture is only valid in the Aharonov-Casher effect induced by spin-orbit interaction only. Unfortunately, this point has not been realized in prior works on the transmission probability in the presence of both SO interaction and Zeeman coupling. We carry out numerical computation to illustrate the joint effects of spin-orbit interaction, Zeeman coupling and magnetic flux. By examining the resonant tunneling of electrons in the weak coupling limit, we establish a connection between the observable time-reversal symmetry breaking effects manifested by the persistent current and by the transmission probability. For a ring formed by two-dimensional electron gas, weComment: 20 pages, 5 figure

Noncyclic geometric phase for neutrino oscillation

We provide explicit formulae for the noncyclic geometric phases or Pancharatnam phases of neutrino oscillations. Since Pancharatnam phase is a generalization of the Berry phase, our results generalize the previous findings for Berry phase in a recent paper [Phys. Lett. B, 466 (1999) 262]. Unlike the Berry phase, the noncyclic geometric phase offers distinctive advantage in terms of measurement and prediction. In particular, for three-flavor mixing, our explicit formula offers an alternative means of determining the CP-violating phase. Our results can also be extended easily to explore geometric phase associated with neutron-antineutron oscillations