共查询到20条相似文献,搜索用时 31 毫秒
1.
PT-symmetric solutions of Schrödinger equation are obtained for the Scarf and generalized harmonic oscillator potentials with the position-dependent mass. A general point canonical transformation is applied by using a free parameter. Three different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter. 相似文献
2.
M. Gadella M. L. Glasser L. M. Nieto 《International Journal of Theoretical Physics》2011,50(7):2144-2152
We study a one-dimensional singular potential plus two types of regular interactions: constant electric field and harmonic
oscillator. In order to search for the bound state energies, we shall use the Lippman-Schwinger Green function technique.
Another direct method will be mentioned for the harmonic oscillator. In the electric field case the unique bound state coincides
with that found in an earlier study as the field is switched off. For non-zero field the ground state is shifted and positive
energy “quasibound states” appear. The harmonic oscillator demonstrates the general result that for a symmetric potential
the odd states are not altered whereas the even states energies are lowered or raised accordingly as the delta perturbation
is attractive or repulsive. No states are created or annihilated. 相似文献
3.
G. Berthier 《Molecular physics》2013,111(2):225-226
We investigate the simple harmonic oscillator in a 1D box, and the 2D isotropic harmonic oscillator problem in a circular cavity with perfectly reflecting boundary conditions. The energy spectrum has been calculated as a function of the self-adjoint extension parameter. For sufficiently negative values of the self-adjoint extension parameter, there are bound states localized at the wall of the box or the cavity that resonate with the standard bound states of the simple harmonic oscillator or the isotropic oscillator. A free particle in a circular cavity has been studied for the sake of comparison. This work represents an application of the recent generalization of the Heisenberg uncertainty relation related to the theory of self-adjoint extensions in a finite volume. 相似文献
4.
Kyu Hwang Yeon Suk Seong Kim Chung In Um Thomas F. George 《International Journal of Theoretical Physics》2003,42(9):2043-2059
Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively. 相似文献
5.
《Physics letters. A》2020,384(25):126577
In this comment we analyze a method for the solution of the eigenvalue equation for three coupled harmonic oscillators proposed recently. We argue that the authors did not obtain the frequencies and coordinates of the normal modes that make the Hamiltonian operator diagonal but merely six transcendental equations for the relevant parameters that they did not attempt to solve. We derive the conditions for the existence of bound states that the authors did not appear to be able to obtain probably because of the complexity exhibited by those equations. 相似文献
6.
7.
The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the
classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states
for time-dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a
demonstration of our general approach. 相似文献
8.
A new single-particle basis is proposed for use in weakly bound nuclei far from the valley of beta stability.The basis, obtained by applying a local-scaling point transformation to the states of a harmonic oscillator potential, can be tailored to have the correct asymptotic properties for weakly bound systems.We first present a test of the basis and then apply it in Hartree-Fock-Bogolyubov calculations of the even Mg isotopes, from the proton drip line to the neutron drip line. 相似文献
9.
The dynamical invariant for a general time-dependent harmonic oscillator is constructed by making use of two linearly independent solutions to the classical equation of motion. In terms of this dynamical invariant we define the time-dependent creation and annihilation operators and relevantly introduce even and odd coherent states for time dependent harmonic oscillator. The mathematical and quantum statistical properties of these states are discussed in detail. The harmonic oscillator with periodically varying frequency is treated as a demonstration of our general approach. 相似文献
10.
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and squeezed reference frames in the system??s phase space. For some specific oscillator states like coherent states and nth excited states, the tomographic-probability distributions (called the state tomograms) are found in an explicit form. The evolution equation for the tomograms is discussed for the classical and quantum driven oscillators, and the tomographic propagator for this equation is studied. 相似文献
11.
Gauge covariant construction of the coherent states for a time-dependent harmonic oscillator by algebraic dynamical method 总被引:5,自引:0,他引:5
Lian-Fu Wei Shun-Jin Wang Quan-Lin Jie 《Zeitschrift für Physik B Condensed Matter》1997,102(4):541-543
Time-dependent coherent states for a time-dependent harmonic oscillator are constructed in the framework of algebraic dynamics. These coherent states are gauge-covariant, and its time evolution is governed only by the solutions of a linear differential equation which describes the motion of the corresponding classical timedependent harmonic oscillator. Its non-classical and quantum statistical properties can thus be controlled by a proper choice of the frequency of the harmonic oscillator. Our coherent states reduce to Glauber coherent states in the case as the frequency is independent of time. 相似文献
12.
The Expansion Method of Mixed Basis Vectors of Lower-energy States and Harmonic Oscillators in Calculation of Bound States of Few-Body Systems 下载免费PDF全文
In this paper,the harmonic oscillator approach to the bound states of few-body ststems is developed and the lower-energy states are introduced as basis vectors and mixed with a part of harmonic oscillator vectors to calculate the binding energy.The lower energy levels of 3-α system and 9Be are presented and compared with experiments or other calculations.The results are satisfactory. 相似文献
13.
We discuss the arising of bound states solutions of the Schrödinger equation due to the presence of a Coulomb-type potential induced by the interaction between a moving electric quadrupole moment and a magnetic field. Furthermore, we study the influence of the Coulomb-type potential on the harmonic oscillator by showing a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system, whose meaning is that not all values of the angular frequency are allowed. 相似文献
14.
提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质.
关键词:
类Quesne环状球谐振子势
Dirac方程
赝自旋对称性
束缚态 相似文献
15.
Bound states of the Klein-Gordon and Dirac equations for scalar and vector harmonic oscillator potentials 下载免费PDF全文
We give the exact bound states of the Klein-Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials. 相似文献
16.
《Physics letters. A》2006,360(2):228-233
A potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the variation of the energy of the bound states are calculated as a function of the well-width and mass. 相似文献
17.
The quantum formalism permits one to discriminate sometimes between any set of linearly independent pure states with certainty. We obtain the maximum probability with which a set of equally likely, symmetric, linearly independent states can be discriminated. The form of this bound is examined for symmetric coherent states of a harmonic oscillator or field mode. 相似文献
18.
M. Kleber 《Zeitschrift für Physik A Hadrons and Nuclei》1970,239(5):395-408
The Schrödinger equation is studied in a finite subspace of the Hilbert space. The truncation of the configuration space makes the (effective) interaction energy-dependent. This dependency is investigated. An analytic expression for the matrix elements of the effective interaction is established for the schematic model, for the displaced harmonic oscillator, for a simple random-phase problem and for a pairing force model. Thereby the phase transitions from bound to unbound states and from normal to superconducting states are analysed. 相似文献
19.
RUAN Dong SUN Hong-Zhou 《理论物理通讯》2005,44(3):499-504
In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2) or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator. 相似文献
20.
RUAN Dong SUN Hong-Zhou 《理论物理通讯》2005,44(9)
In this paper N = 4 supersymmetry of generalized Morse oscillators in one dimension is studied. Both bound states and scattering states of its four superpartner Hamiltonians are analyzed by using unitary irreducible representations of the noncompact Lie algebra su(1,1). The spectrum-generating algebra governing the Hamiltonian of the N = 4 supersymmetric Morse oscillator is shown to be connected with the realization of Lie superalgebra osp(1,2)or B(0,1) in terms of the variables of a supersymmetric two-dimensional harmonic oscillator. 相似文献