共查询到20条相似文献,搜索用时 0 毫秒
1.
BAI Zhan-Wu 《理论物理通讯》2008,49(1):137-142
We investigate the low-temperature statistical properties of a harmonic oscillator coupled to a heat bath, where the low-frequency spectrum vanishes. We obtain the exact result of the zero point energy. Due to the low frequency shortage of environmental oscillators' spectral density, the coordinate and momentum correlation functions decay as T^-4 arid T^-6 respectively at zero temperature, where T is the correlation time. The low-temperature behavior of the mean energy does not violate the third law of thermodynamics, but differs largely from the Ohmic spectrum case. 相似文献
2.
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
3.
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
4.
We consider the H-theorem in an isolated quantum harmonic oscillator through the time-dependent Schrödinger equation. The effect of potential in producing entropy is investigated in detail, and we found that including a barrier potential into a harmonic trap would lead to the thermalization of the system, while a harmonic trap alone would not thermalize the system. During thermalization, Shannon entropy increases, which shows that a microscopic quantum system still obeys the macroscopic thermodynamics law. Meanwhile, initial coherent mechanical energy transforms to incoherent thermal energy during thermalization, which exhibiting the decoherence of an oscillating wave packet featured by a large decreasing of autocorrelation length. When reaching thermal equilibrium, the wave packet comes to a halt, with the density distributions both in position and momentum spaces well-fitted by a microcanonical ensemble of statistical mechanics. 相似文献
5.
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
6.
Quantum uncertainties of the confined Harmonic Oscillator in position,momentum and phase‐space 下载免费PDF全文
Quantum uncertainties in position, momentum and phase‐space are studied in the confined Harmonic Oscillator. Standard deviations and Shannon entropies are used to quantify these uncertainties and their behaviors are compared and contrasted. We observe a minimum in the momentum space Shannon entropy as the box length is increased, a feature that is not present in the momentum space standard deviation. The behaviors of the standard deviation product and the Shannon entropy sum, which form the basis of uncertainty relationships, are also analyzed. Maxima are observed in the product as the box length increases in sharp contrast to the entropy sum. The relationship between these behaviors and that of the Shannon entropy of the phase‐space Wigner function is analyzed and discussed. An analysis of the energetic components is also performed. The results reinforce the idea that the confined Harmonic Oscillator can be considered as an intermediate model which interpolates between the Particle in a Box Model and the Harmonic Oscillator and thus contains characteristics of both models.
7.
The solutions of the Schrodinger equation with quantum mechanical gravitational potential plus harmonic oscillator potential have been presented using the parametric Nikiforov-Uvarov method. The bound state energy eigen values and the corresponding un-normalized eigen functions are obtained in terms of Laguerre polynomials. Also a special case of the potential has been considered and its energy eigen values are obtained. 相似文献
8.
We consider the relations between the theory of quantum nonstationary damped oscillator and nonstationary Casimir effect in
view of the problem of photon creation from vacuum inside the cavity with periodical time-dependent conductivity of a thin
semiconductor boundary layer, which simulates periodical displacements of the cavity boundaries. We develop a consistent model
of quantum damped harmonic oscillator with arbitrary time-dependent frequency and damping coefficients within the framework
of Heisenberg-Langevin equations with two noncommuting delta-correlated noise operators. For the minimum noise set of correlation
functions, whose time dependence follows that of the damping coefficient, we obtain the exact solution, which is a generalization
of the Husimi solution for undamped nonstationary oscillator. It yields the general formula for the photon-generation rate
under the resonance condition in the presence of dissipation. We obtain a simple approximate formula for a time-dependent
shift of the complex resonance frequency. It depends only on the total energy of a short laser pulse (which creates an effective
time-dependent electron-hole “plasma mirror” on the semiconductor-slab surface) and the recombination time. We show that damping
due to a finite conductivity of the material significantly diminishes the photon-generation rate in the selected field mode
of the cavity. Nonetheless, we have found optimum values of the parameters (laser pulse power, recombination time, and cavity
dimensions), for which the effect of photon generation from vacuum could be observed in the experimental set-up proposed in
the University of Padua. We also provide with a list of publications from 2001 to 2005 devoted to the study on quantum-field
interactions with moving boundaries (mirrors).
Dedicated to Prof. Vladimir I. Man'ko on the occasion of his 65th birthday. 相似文献
9.
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
10.
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
11.
Alexis Pokrovski 《Mathematical Physics, Analysis and Geometry》2007,10(3):197-203
Let be the spectrum of in L
2(ℝ), where q is an even almost-periodic complex-valued function with bounded primitive and derivative. It is known that , where is the spectrum of the unperturbed operator. Suppose that the asymptotic approximation to the first asymptotic correction
is given. We prove the formula that recovers the frequencies and the Fourier coefficients of q in terms of Δμ
n
.
相似文献
12.
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
13.
M. Genovese 《Foundations of Physics Letters》2003,16(5):505-511
In this letter we reconsider the proposal of Ref. [1] about a quantum measurement performed by a DNA molecule in aqueous solution as a tool for illustrating specific difficulties of some approach to quantum measurement problem. Our main result is that, when the interaction of DNA and enzymes with aqueous environment is properly kept into account, no real problem appears for any specific model. 相似文献
14.
在利用Wigner函数性质的基础上, 考虑到空间变量的对易关系中包含了坐标 坐标的非对易性, 得到了带电线性谐振子在非对易空间中的Wigner函数。 Based on the property of wigner function, the Wigner function of charged Linear Harmonic Oscillator in non commutative space was obtained by considering the noncommutative of the coordinate coordinate in the relation of space variable. 相似文献
15.
Willem M. de Muynck 《Foundations of Physics》2004,34(5):717-770
The Copenhagen interpretation is critically considered. A number of ambiguities, inconsistencies and confusions are discussed. It is argued that it is possible to purge the interpretation so as to obtain a consistent and reasonable way to interpret the mathematical formalism of quantum mechanics, which is in agreement with the way this theory is dealt with in experimental practice. In particular, the essential role attributed by the Copenhagen interpretation to measurement is acknowledged. For this reason it is proposed to refer to it as a neo-Copenhagen interpretation. 相似文献
16.
17.
We present a critique of the many-world interpretation of quantum mechanics, based on different “pictures” that describe the time evolution of an isolated quantum system. Without an externally imposed frame to restrict these possible pictures, the theory cannot yield non-trivial interpretational statements. This is analogous to Goodman’s famous “grue-bleen” problem of language and induction. Using a general framework applicable to many kinds of dynamical theories, we try to identify the kind of additional structure (if any) required for the meaningful interpretation of a theory. We find that the “grue-bleen” problem is not restricted to quantum mechanics, but also affects other theories including classical Hamiltonian mechanics. For all such theories, absent external frame information, an isolated system has no interpretation. 相似文献
18.
The implications of the Copenhagen Variant of the Modal Interpretation of Quantum Mechanics are studied in the context of the quantum theory of measurement. Two formulations of this interpretation are discussed. Both of them imply specifications of the notion of measurement which go beyond the minimal calibration condition of a measurement. The weaker one implies some algebraic and topological constrains on the measurement coupling, whereas the stronger formulation of the same interpretation implies that measurements are necessarily of the first kind. 相似文献
19.
Given a constant of motion for the one-dimensional harmonic oscillator with linear dissipation in the velocity, the problem to get the Hamiltonian for this system is pointed out, and the quantization up to second order in the perturbation approach is used to determine the modification on the eigenvalues when dissipation is taken into consideration. This quantization is realized using the constant of motion instead of the Hamiltonian.
PACS: 03.20.+i, 03.30.+p, 03.65.−w,03.65.Ca 相似文献
20.
Consider the perturbed harmonic oscillator Ty = -y" + x2y + q(x)y on L2(R) where the real potential q satisfy some assumption on infinity (the case q L2(R), (t+1)-rdt), r < 1 is covered). 相似文献