相关论文: Quantum Correction in Exact Quantization Rules

The quasilinearization method (QLM) of solving nonlinear differential equations is applied to the quantum mechanics by casting the Schr\"{o}dinger equation in the nonlinear Riccati form. The method, whose mathematical basis in physics was…

We consider a non relativistic charged particle in a 1-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) time depending electric field. It is represented by a complex…

Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg…

In this thesis, we study a quantization condition in relation to the solvability of Schr\"{o}dinger equations. This quantization condition is called the SWKB (supersymmetric Wentzel-Kramers-Brillouin) quantization condition and has been…

We carry out an exact quantization of a PT symmetric (reversible) Li\'{e}nard type one dimensional nonlinear oscillator both semiclassically and quantum mechanically. The associated time independent classical Hamiltonian is of non-standard…

The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the…

We develop a method for computing exact one-loop quantum corrections to the energies of static classical backgrounds in renormalizable quantum field theories. We use a continuum density of states formalism to construct a regularized Casimir…

The N-quantum approach (NQA) to quantum field theory uses the complete and irreducible set of in or out fields, including in or out fields for bound states, as standard building blocks to construct solutions to quantum field theories. In…

Vacuum polarisation (VP) and electron self energy (SE) are implemented and evaluated as quantum electrodynamic (QED) corrections in a (quasi-relativistic) two-component zeroth order regular approximation (ZORA) framework. For VP, the…

The influence of continuous measurements of energy with a finite accuracy is studied in various quantum systems through a restriction of the Feynman path-integrals around the measurement result. The method, which is equivalent to consider…

Semiclassical quantization is exact only for the so called \emph{solvable} potentials, such as the harmonic oscillator. In the \emph{nonsolvable} case the semiclassical phase, given by a series in $\hbar$, yields more or less approximate…

It is proposed that the Schrodinger equation for a free point particle has non-linear corrections which depend on the mass of the particle. It is assumed that the corrections become extremely small when the mass is much smaller or much…

Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that…

We generalize the exact quantization rule to multiple turning points, which are all on the real axis and are even in number. We found that when we take wave functions of different energy levels, they are stable between two adjacent turning…

Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a…

For zero energy, $E=0$, we derive exact, classical and quantum solutions for {\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$, $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions…

In this study, we employ exact quantization rule (EQR) to derive the analytical approximate l-wave solutions of the Schrodinger equation with the general molecular oscillator (GMO). The energy eigenvalues equation and the corresponding wave…

The exact solutions of the one-dimensional Klein-Gordon equation for the Rosen-Morse type potential with equal scalar and vector potentials are presented. First we briefly review Nikiforov-Uvarov mathematical method. Using this method,…

We present exact solutions of the Schr\"odinger equation for a quantum system with complex mass subjected to a complex Morse potential in the extended complex phase space. The normalized eigenfunctions and corresponding eigenspectra are…

This analysis is concerned with the controllability of quantum systems in the case where the standard dipolar approximation, involving the permanent dipole moment of the system, is corrected with a polarizability term, involving the field…