共查询到20条相似文献,搜索用时 15 毫秒
1.
By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well. 相似文献
2.
In cylindrical coordinate, exact wave functions
of the two-dimensional time-dependent harmonic oscillator in
a time-dependent magnetic field are derived by using the trial
function method. Meanwhile, the exact classical solution as well
as the classical phase is obtained too. Through the Heisenberg
correspondence principle, the quantum solution and the classical
solution are connected together. 相似文献
3.
Exact wave functions of the forced time-dependent two-dimensional harmonic oscillator in a static magnetic field are derived by unitary transformation. The geometrical phase induced by the driving force is the phase of the de Broglie wave associated with the particle moving according to the classical equation. Extending the idea of the Heisenberg correspondence principle to the time-dependent system, the exact classical solution
obtained from quantum matrix elements. 相似文献
4.
The exact solutions with arbitrary permutation symmetry to the threebody Schrödinger equation for the harmonic oscillator are presented completely. 相似文献
5.
非球谐振子势的精确解 总被引:6,自引:0,他引:6
严格求解了三维非球谐振,势的Schrodinger方程给出了精确的能谱方程和归一化的径向波函数.获得了径向幂次算符rs的矩阵元和平均值的计算公式及其递推关系. 相似文献
6.
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
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.
The propagator for a time-dependent damped harmonic oscillator with a force quadratic in velocity isobtained by making a specific coordinate transformation and by using the method of time-dependent invariant. 相似文献
9.
Y. Bouguerra M. Maamache A. Bounames 《International Journal of Theoretical Physics》2006,45(9):1791-1797
We use the Lewis-Riesenfeld theory to determine the exact form of the wavefunctions of a two-dimensionnal harmonic oscillator with time-dependent mass and frequency in presence of the Aharonov-Bohm effect (AB). We find that the auxiliary equation is independent of the AB magnetic flux. In the particular case of quantized AB magnetic flux the wavefunctions coincide exactly with the wavefunctions of the 2D time-dependent harmonic oscillator.
PACS: 03.65Ge; 03.65Fd; 03.65Bz 相似文献
10.
QIAN Shang-Wu WANG Jing-Shan 《理论物理通讯》2008,49(2):308-310
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived. 相似文献
11.
An equivalent circuit model of millimeter wave second harmonic oscillator stabilized with a transmission cavity has been proposed
for constructing analytical formulations between performance parameters of the oscillator and parameters of the circuit. The
model consists of an equivalent circuit of fundamental wave and that of second harmonic wave. Each of the circuits comprises
circuit models of main cavity, transmission waveguide, and transmission cavity. Absorbing material placed between the transmission
waveguide and the transmission cavity can suppress additional resonances originated from transmission cavity. The behavior
of the second harmonic oscillator can be effectively described by the circuit model. Furthermore, based on this model, mechanical
tuning characteristics have been studied at first, and then analytical formulas for quality factor and efficiency depending
on circuit parameters have been derived. The circuit parameters can be conveniently extracted by electromagnetic field simulation.
Hence the formulas exhibit both compact form and enough accuracy. Thereafter, general rules of performance parameters varying
with circuit parameters have been deduced for the harmonic oscillators. Then some design considerations have been derived
according to the corresponding analysis. The equivalent circuit model is useful for designing and adjusting millimeter wave
second harmonic stabilizing oscillator with a transmission cavity. 相似文献
12.
首先介绍了Wigner函数的基本性质以及以Wigner函数为基础的相空间定态微扰理论,然后将其应用到一维无限深势阱和谐振子。 推导出一维无限深势阱所对应的Wigner函数,而且发现了存在于其纯态Wigner函数中奇特的压缩效应, 并利用不确定性关系给予了解释。同时计算出一维无限深势阱和谐振子在微扰的作用下,相应Wigner函数和能级的修正。 In this article, the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one dimensional infinite potential well and one dimensional harmonic oscillator, and then the particular Wigner function of one dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which, simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one dimensional infinite potential well and one dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. 相似文献
13.
一维时间相关的经典谐振子是一个SU(1,1) 非自治经典系统,物理上十分有用,而数学上难于得到其精确解析解. 首次把新颖的代数动力学方法用于经典动力学系统,得到了这个模型的一般精确解;当时间相关的弹性系数为某些初等函数时,给出了精确解的解析形式. 这是关于这一问题的重要结果. 从精确解出发,推导出最近文献中提出的"解析近似解",并指出该近似解的适用条件. 相似文献
14.
讨论势函数为V(ρ)=2ρ λρα的非谐振子的Schr dinger方程。当α=2时其有Hamiltonian量的精确束缚态解。当α3时其有Hamiltonian量的微扰解,尤其是它的一阶、两阶的能量修正及零级、一级波函数。 相似文献
15.
A generalized Talmi-Moshinsky transformation relating one-dimensional harmonic oscillator product states with different sets of Jacobian coordinates is derived for systems composed of an arbitrary number of particles with arbitrary masses. With the help of our method the multidimensional integral which must be performed to evaluate an N-particle matrix element can be transformed into a sum of products of one-dimensional integrals. 相似文献
16.
A one-dimensional harmonic oscillator with position-dependent effective mass is studied. We quantize the oscillator to obtain a quantum Hamiltonian, which is manifestly Hermitian in configuration space, and the exact solutions to the corresponding Schrödinger equation are obtained analytically in terms of modified Hermite polynomials. It is shown that the obtained solutions reduce to those of simple harmonic oscillator as the position dependence of the mass vanishes. 相似文献
17.
Min-Cang Zhang 《International Journal of Theoretical Physics》2009,48(9):2625-2632
The pseudospin symmetry for a ring-shaped non-spherical harmonic oscillator potential is investigated by solving the Dirac
equation with equal mixture of scalar and vector potentials with opposite signs. The normalized spinor wave function and energy
equation are obtained, the algebraic property of the energy equation and some particular cases are also discussed. 相似文献
18.
Diego Julio Cirilo-Lombardo 《Foundations of Physics》2007,37(8):1149-1180
Relativistic geometrical action for a quantum particle in the superspace is analyzed from theoretical group point of view.
To this end an alternative technique of quantization outlined by the authors in a previous work and, that is, based in the
correct interpretation of the square root Hamiltonian, is used. The obtained spectrum of physical states and the Fock construction
consist of Squeezed States (SS) which correspond to the representations with the lowest weights and with four possible (non-trivial) fractional representations for the group decomposition of the spin structure. From the theory
of semi-groups the analytical representation of the radical operator in the superspace is constructed, the conserved currents
are computed and a new relativistic wave equation is proposed and explicitly solved for the time dependent case. The relation
with the Relativistic Schr?dinger equation and the Time-dependent Harmonic Oscillator (TDHO) is analyzed and discussed.
An erratum to this article can be found at 相似文献
19.
LIN Qiong-Gui 《理论物理通讯》2002,38(12)
A nonrelativistic charged particle moving in an anisotropic harmonic oscillator potential plus a homogeneousstatic electromagnetic field is studied. Several configurations of the electromagnetic field are considered. The Schrodingerequation is solved analytically in most of the cases. The energy levels and wave functions are obtained explicitly. Insome of the cases, the ground state obtained is not a minimum wave packet, though it is of the Gaussian type. Coherentand squeezed states and their time evolution axe discussed in detail. 相似文献
20.
LIN Qiong-Gui 《理论物理通讯》2002,38(6):667-670
A nonrelativistic charged particle moving in an anisotropic harmonic
oscillator potential plus a homogeneous static electromagnetic field
is studied. Several configurations of the electromagnetic field are
considered. The Schrödinger equation is solved analytically in most
of the cases. The energy levels and wave functions are obtained
explicitly. In some of the cases, the ground state obtained is not a
minimum wave packet, though it is of the Gaussian type. Coherent and
squeezed states and their time evolution are discussed in detail. 相似文献