相关论文: SWKB for the Angular Momentum
We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
This work reports quantum mechanical and semiclassical WKB calculations for energies and wave functions of high-lying $^2\Sigma$ states of H$_2^+$ in atomic units. The high-lying states presented lie in an unexplored regime, corresponding…
The bound state wave functions for a wide class of exactly solvable potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is shown that, exploiting the singularity structure of the quantum momentum function, until now…
The independent eigenstates of the total orbital angular momentum operators for a three-body system in an arbitrary D-dimensional space are presented by the method of group theory. The Schr\"{o}dinger equation is reduced to the generalized…
We derive the semiclassical WKB quantization condition for obtaining the energy band edges of periodic potentials. The derivation is based on an approach which is much simpler than the usual method of interpolating with linear potentials in…
Harmonic inversion is introduced as a powerful tool for both the analysis of quantum spectra and semiclassical periodic orbit quantization. The method allows to circumvent the uncertainty principle of the conventional Fourier transform and…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
We calculate the orbital angular momentum of the `quark' in the scalar diquark model as well as that of the electron in QED (to order $\alpha$). We compare the orbital angular momentum obtained from the Jaffe-Manohar decomposition to that…
In the framework of the deformed quantum mechanics with minimal length, we consider the motion of a non-relativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function…
We uncover an inconsistency in the uniform WKB quantization of deformed quantum mechanics.
We generalize the universal effective quantum number introduced earlier for centrally symmetric problems. The proposed number determines the semiclassical quantization condition for axially symmetric potentials.
{}From Feynman's path integral, we derive quasi-classical quantization rules in supersymmetric quantum mechanics (SUSY-QM). First, we derive a SUSY counterpart of Gutzwiller's formula, from which we obtain the quantization rule of Comtet,…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB…
Using a recently proposed classification for the primary translationally shape invariant potentials, we show that the exact quantization rule formulated by Ma and Xu is equivalent to the supersymmetric JWKB quantization condition. The…
By means of numerical solutions of the quantum Hamilton Jacobi equation, a general WKB-like representation for one-dimensional wave functions is obtained. This representation is unique in the classically forbidden regions, while in the…
Time symmetry in quantum mechanics, where the current quantum state is determined jointly by both the past and the future, offers a more comprehensive description of physical phenomena. This symmetry facilitates both forward and backward…
The accurate computation of ground and excited states of many-fermion quantum systems is one of the most consequential, contemporary challenges in the physical and computational sciences whose solution stands to benefit significantly from…
We propose a new approximate series solution of the semiclassical Wigner equation by uniformization of WKB approximations of the Schr\"odinger eigenfunctions.