共查询到20条相似文献,搜索用时 31 毫秒
1.
Bin Kang Cheng 《Physics letters. A》1985,113(6):293-296
By finding a space and time transformation, the exact evaluation of the propagator for the harmonic oscillator with a time-dependent mass by the path integral method becomes possible. We then derive the wavefunctions from the propagator obtained. Finally, the propagator beyond and at caustics is evaluated by using its modified semi-group property and is confirmed by investigating the classical paths with two fixed end-positions. 相似文献
2.
通过正则化变换技巧,寻找到一种对阻尼系数随时间变化的阻尼谐振子直接量子化方案,进而采用高斯型传播子和费曼路径积分方法求出了含时阻尼谐振子的严格波函数,并对波函数的普遍意义,坐标和动量的零点涨落以及两者的不确定关系作了讨论
关键词:
含时阻尼
传播子
费曼路径积分 相似文献
3.
4.
The invariant, propagator, and wavefunction for a variable frequency harmonic oscillator in an electromagnetic field are obtained by making a specific coordinate transformation and by using the method of phase space path integral method. The probability amplitudes for a dissipative harmonic oscillator in the time varying electric field E(t) = E0 sin(Ωt) are obtained. 相似文献
5.
《Physics letters. A》1984,101(9):464-468
Horváthy's modification of Feynman's path integral formula is generalized to the time-dependent forced harmonic oscillator. The propagator at caustics is then obtained by using its modified semi-group property. Finally, with our new formula, the propagator for a charged particle in a time-dependent electromagnetic field is evaluated exactly beyond and at caustics. 相似文献
6.
Jian Jing Shi-Hua Zhao Jian-Feng Chen Zheng-Wen Long 《The European Physical Journal C - Particles and Fields》2008,54(4):685-690
The spectra and wave functions of the 2-dimensional harmonic oscillator in a noncommutative plane are revised by using the
path integral formulation in coordinate space and momentum space, respectively. We perform the path integral formulation in
coordinate space first. Then we study this problem in momentum space. The propagator is computed both in coordinate space
and in momentum space. The modification due to noncommutativity of eigenvalues and eigenfunctions is studied. Both the small
and large noncommutative parameter limits are discussed.
PACS 11.10.Ef 相似文献
7.
Bin Kang Cheng 《International Journal of Theoretical Physics》1984,23(12):1099-1104
Horváthy's modification of Feynman's original method is generalized to the path integral formula of a forced harmonic oscillator. With this new formula the propagator of a harmonic oscillator with memory is evaluated exactly beyond and at caustics.Work supported in part by the Conselho Nacional de Desenvolvimento Cientifico e Tecnólogico (CNPq), Brazil. 相似文献
8.
Path integration of an action representing a harmonic oscillator with a generalized memory is carried out within the framework of Feynman's polygonal approach. The exact propagator obtained is in the form of an exponential integral over a single variable. Closed analytical results are available for special cases of the memory function. 相似文献
9.
10.
We study the evolution of the driven harmonic oscillator in the probability representation of quantum mechanics. We use the photon-number tomographic-probability-distribution function to describe the quantum states of the system. We give a general review of the photon-number tomographic framework, including a discussion on the connection with other representations of quantum mechanics. We find tomograms of coherent states as well as excited states of the harmonic oscillator in an explicit form. We discuss the time evolution of the photon-number tomograms and transforms of the propagators for different representations of quantum mechanics. We obtain the propagator for the photon-number tomographic-distribution function for the case of the driven oscillator in an explicit form. 相似文献
11.
We obtain the Hamilton operator of the Calogero-Moser quantum system in an external quadratic potential by conjugating the radial part for the action of SO(n) by conjugacy of the Hamilton operator of the quantum harmonic oscillator on the Euclidean vector space of real symmetric matrices. Then, with Mehler's formula, we derive the propagator of the problem. We also investigate some schemes to change the interaction constant. For two-particle systems, we obtain explicit formulae, whereas for many-particle systems, we reduce the computation of the propagator to finding a definite integral. We give also the short time approximation, the energy levels and the trace of the propagation operator. 相似文献
12.
In this paper we consider a neutral spinning particle in interaction with a linear increasing rotating magnetic field and
a scalar harmonic potential using the path integral formalism. The Pauli matrices which describe the spin dynamics are replaced
by two fermionic oscillators via the Schwinger’s model. The calculations are carried out explicitly using fermionic exterior
current sources. The problem is then reduced to that of a spinning forced harmonic particle whose spin is coupled to exterior
derivative current sources. The result of the propagator is given as a series which is exactly summed up by means of the Laplace
transformation and the use of some recurrence formula of the oscillator wave functions. The energy spectrum and the corresponding
wave functions are also deduced. 相似文献
13.
14.
文章用Schwinger方法与Makri等人发展的幂级数展开法研究了周期阻尼简谐振子的传播子.研究表明,这两种方法所获得的短时传播子非常接近,但是后者比前者要简单得多,这给研究复杂系统的传播子提供了一个简单可靠的方法. 相似文献
15.
Tunneling in a “breathing” double well: Adiabatic and antiadiabatic limits and tunneling suppression
Tunneling in a piecewise harmonic potential coupled to a harmonic oscillator is considered by means of the path integral technique. The reduced propagator for the tunneling particle is calculated explicitly and the tunneling splitting is found in semiclassical approximation. The result holds for arbitrary values of the parameters of the system. From this the adiabatic and antiadiabatic approximations are obtained as particular cases and compared with the results obtained differently. The limit of a strong interaction is also considered. It is found that for strong interaction or equivalently for the harmonic frequency tending to zero the preexponential factor in the tunneling splitting tends to zero which results in a suppression of tunneling. Implications of this result for tunneling in a more general potential are discussed. 相似文献
16.
M. Boudjema-Bouloudenine T. Boudjedaa A. Makhlouf 《The European Physical Journal C - Particles and Fields》2006,46(3):807-816
We have applied the Schwinger action principle to general one-dimensional (1D), time-dependent quadratic systems via linear
quantum canonical transformations, which allowed us to simplify the problems to be solved by this method. We show that while
using a suitable linear canonical transformation, we can considerably simplify the evaluation of the propagator of the studied
system to that for a free particle. The efficiency and exactness of this method is verified in the case of the simple harmonic
oscillator. This technique enables us to evaluate easily and immediately the propagator in some particular cases such as the
damped harmonic oscillator, the harmonic oscillator with a time-dependent frequency, and the harmonic oscillator with time-dependent
mass and frequency, and in this way the propagator of the forced damped harmonic oscillator is easily calculated without any
approach.
PACS 02.30.Xx, 03.65.-w, 03.65.Ca 相似文献
17.
We study the asymptotic dynamics of a driven spin-boson system
where the environment is formed by a broadened localized mode.
Upon exploiting an exact mapping, an equivalent formulation of the
problem in terms of a quantum two-state system (qubit) coupled to
a harmonic oscillator which is itself Ohmically damped, is found.
We calculate the asymptotic population difference of the two
states in two complementary parameter regimes. For weak damping
and low temperature, a perturbative Floquet-Born-Markovian master
equation for the qubit-oscillator system can be solved. We find
multi-photon resonances corresponding to transitions in the
coupled quantum system and calculate their line-shape
analytically. In the complementary parameter regime of strong
damping and/or high temperatures, non-perturbative real-time path
integral techniques yield analytic results for the resonance line
shape. In both regimes, we find very good agreement with exact
results obtained from a numerical real-time path-integral
approach. Finally, we show for the case of strong detuning between
qubit and oscillator that the width of the n-photon resonance
scales with the nth Bessel function of the driving strength in
the weak-damping regime. 相似文献
18.
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
19.
《Physics letters. A》1987,123(1):9-13
We show that, by using a convenient space-time transformation, we can considerably simplify the evaluation of the exact transformation function (or propagator) for a time-dependent mass, subject to a time-varying, forced harmonic oscillator potential, obtained through the Schwinger action principle. Overall, we demonstrate that such a transformation function can be obtained from that for a free particle (with unit mass) in the new space-time coordinate system. 相似文献
20.
Mario Bergeron 《Fortschritte der Physik》1992,40(2):119-159
Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP1 model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral. 相似文献