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关于自由粒子量子态数的计算和讨论 总被引:4,自引:0,他引:4
在系统热力学量的统计计算中,粒子的量子态密度(单位能量间隔中的状态数目)的计算占有重要地位.粒子的态密度与粒子运动空间的维度性有关,与粒子的能谱(粒子的动量能量关系)有关,且与粒子的自旋有关.本文对自由粒子(视为质点)的态密度计算作普遍性的讨论. 相似文献
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一维无限深势阱中本征态粒子的动量呈现负无穷到正无穷且有无数个节点的对称连续分布.本征态粒子的无量纲动量概率密度分布一般由两个主峰和无数的次峰组成,经典动量和最概然动量都分布在主峰区域内.数值计算结果表明动量谱在两个主峰区域内的概率极限值约为0.902 8,测量所包含的次峰数量越多则粒子出现的概率越接近1.粒子经典动量分布是量子动量分布在高测量精度和大量子数条件下的极限. 相似文献
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量子光学中的Rabi模型描述了一个与量子谐振子耦合的两能级系统,当耦合强度与振子频率相当时,会产生丰富的物理现象.本文研究了谐波势阱中具有拉曼诱导自旋轨道耦合的Bose气体,通过将受限系统映射为Rabi模型,引入量子光学中的平移Fock态利用变分方法求解了系统的本征能态和基态,发现左右平移Fock态的奇宇称叠加态能量低于平移态的能量,并分别研究了粒子在动量和坐标空间的动力学Zitterbewegung振荡特性以及原子极化的动力学,给出了一个直观清晰的物理图像,与相关实验的结果定性一致.本文的研究结果有助于进一步研究量子光学领域目前难以实现的深度强耦合参数区域的量子Rabi模型,对冷原子物理的研究也有一些借鉴和启发. 相似文献
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给出一种不依赖于具体动量图象求粒子反应中初态粒子的阈能和末态粒子最大能量的方法,并就常见的粒子反应作了讨论。 相似文献
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G.-L. Ingold A. Wobst Ch. Aulbach P. Hänggi 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,30(2):175-179
In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast,
the Aubry-André model with its quasiperiodic potential shows a transition from extended to localized states. The difference
between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite
resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for
the delocalization of a quantum particle.
Received 3 May 2002 / Received in final form 2 October 2002 Published online 29 November 2002 相似文献
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In a recent paper, we presented a nonperturbative higher order Generalized Uncertainty Principle (GUP) that is consistent with various proposals of quantum gravity such as string theory, loop quantum gravity, doubly special relativity, and predicts both a minimal length uncertainty and a maximal observable momentum. In this Letter, we find exact maximally localized states and present a formally self-adjoint and naturally perturbative representation of this modified algebra. Then we extend this GUP to D dimensions that will be shown it is noncommutative and find invariant density of states. We show that the presence of the maximal momentum results in upper bounds on the energy spectrum of the free particle and the particle in box. Moreover, this form of GUP modifies blackbody radiation spectrum at high frequencies and predicts a finite cosmological constant. Although it does not solve the cosmological constant problem, it gives a better estimation with respect to the presence of just the minimal length. 相似文献
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J. Maćkowiak 《Physica A》1983,117(1):47-75
The thermodynamic limit of free energy density is investigated for quantum systems of n particles obeying Boltzmann, Fermi and Bose statistics, interacting via spin-independent 2-body bounded separable potentials and confined to a bounded region Λ ? Rv. The technique used exploits the Feynman-Kac theorem in finite volume and the saddle-point method of Tindemans and Capel. It is shown that the limiting free energy density of such systems is equal to that of a system of noninteracting particles subject to a mean field which is equal to the averaged 2-body interaction. The equations for the mean field of n particles obeying Boltzmann, Fermi or Bose statistics represent self-consistent field problems and their forms comply with the well-known theorems on mean occupation numbers of single-particle eigenstates of ideal quantum gases at inverse temperature β. 相似文献
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A relativistic phase-space representation for a class of observables with matrix-valued Weyl symbols proportional to the identity matrix (charge-invariant observables) is proposed. We take into account the nontrivial charge structure of the position and momentum operators. The evolution equation coincides with its analog in relativistic quantum mechanics with nonlocal Hamiltonian under conditions where particle-pair creation does not take place (free particle and constant magnetic field). The differences in the equations are connected with the peculiarities of the constraints on the initial conditions. An effective increase in coherence between eigenstates of the Hamiltonian is found and possibilities of its experimental observation are discussed. 相似文献
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Quench dynamics of two one-dimensional harmonically trapped bosons bridging attraction and repulsion
ABSTRACTWe unravel the nonequilibrium quantum dynamics of two harmonically confined bosons in one spatial dimension when performing an interaction quench from finite repulsive to attractive interaction strengths and vice versa. A closed analytical form of the expansion coefficients of the time-evolved two-body wavefunction is derived, while its dynamics is determined in terms of an expansion over the postquench eigenstates. For both quench scenarios the temporal evolution is analysed by inspecting the one- and two-body reduced density matrices and densities, the momentum distribution and the fidelity. Resorting to the fidelity spectrum and the eigenspectrum we identify the dominant eigenstates of the system that govern the dynamics. Monitoring the dynamics of the above-mentioned observables we provide signatures of the energetically higher-lying states triggered by the quench. 相似文献
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Jagannath Thakur 《Pramana》1991,37(1):21-38
We consider the quantum mechanics of directly interacting relativistic particles of spin-zero and spin-half. We introduce
a scalar product in the vector space of physical states which is finite, positive definite and relativistically invariant
and keeps orthogonal eigenstates of total four momentum belonging to different eigenvalues. This allows us to show that the
vector space of physical states is, in fact, a Hilbert space. The case of two particles is explicitly considered and the Cauchy
problem of physical wave function illustrated. The problem of a spin-1/2 particle interacting with a spin-zero particle is
considered and a new equation is proposed for two spin-1/2 particles interacting via the most general form of interaction
possible. The restrictions due to Hermiticity, space inversion and time reversal invariance are also considered. 相似文献
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This paper introduces the concepts of asymptotic localization and separation, and shows that quantum mechanical states exist which are asymptotically localizable and separable; these are states with finite and disjoint momentum ranges respectively. All this applies whether the quantum particle concerned is free or is in a potential. 相似文献
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We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In particular, we investigate the prerequisites for thermalization, focusing on the statistical properties of the time-averaged density matrix and of the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the microcanonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some nonintegrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two scenarios for thermalization. 相似文献
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A single particle magneto-confined in a one-dimensional (1D) quantum
wire experiences a harmonic potential, and imposing a sharply
focused laser beam on an appropriate site shapes a $\delta$
potential. The theoretical investigation has demonstrated that for a
sufficiently strong $\delta$ pulse the quantum motional stationary
state of the particle is one of the eigenstates of the free harmonic
oscillator, and it is determined by the site of the laser beam
uniquely, namely a quantum state is admissible if and only if the
laser site is one of its nodes. The numerical computation shows that
all the nodes of the lower energy states with quantum numbers $n \le
20$, except the coordinate origin, are mutually different. So we can
manipulate the multiphoton transitions between the quantum states by
adjusting the position of the laser $\delta$ pulse and realize the
transition from an unknown higher excitation state to a required
lower energy state. 相似文献