共查询到20条相似文献,搜索用时 15 毫秒
1.
J. Cislo J. ?opuszański 《Reports on Mathematical Physics》2003,52(1):35-41
An example of nonequivalent but s-equivalent Lagrange function for a one-dimensional harmonic oscillator are presented and discussed. The quantum approach displays a quite different structure from the usual standard one. 相似文献
2.
2000年以来, 有关非对易空间的各种物理问题一直是研究的热点, 并在量子力学、场论、凝聚态物理、天体物理等各领域中已被广泛地探讨. 采用统计物理方法讨论非对易效应对谐振子体系热力学性质的影响. 先以对易相空间中确定二维和三维谐振子的配分函数求出谐振子体系的热力学函数; 非对易相空间中的坐标和动量通过坐标-坐标和动量-动量之间的线性变换而以对易相空间中的坐标和动量来表示; 最终以非对易相空间中求出配分函数来讨论非对易效应对谐振子体系热力学性质的影响. 结果显示, 在非对易相空间中谐振子体系的配分函数和熵表达式均包含因非对易引起的修正项. 从分析结果得出如下结论: 非对易效应对谐振子的配分函数和熵函数等微观状态函数有一定的影响, 但对谐振子体系的内能、热容量等宏观热力学函数没有影响. 研究结果只是对应于满足玻尔兹曼统计的经典体系, 对于满足费米-狄拉克和玻色-爱因斯坦统计的量子体系需进一步推广研究. 相似文献
3.
《Physics letters. A》2019,383(24):2836-2838
In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman Lagrangian. In particular, we prove that no square integrable vacuum exists for the natural ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous. 相似文献
4.
In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta. 相似文献
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In this paper we study a certain class of generalized perturbation problem for the isotropic three dimensional harmonic oscillator,
forl=0 states only, for all excited states. The efficacy of our formalism is tested by studying the Killingbeck potential in detail.
We also briefly present our results using the diagonal Padé approximants. 相似文献
7.
In this paper a new ring-shaped harmonic oscillator for spin 1/2 particles is studied, and the corresponding eigenfunctions and eigenenergies are obtained by solving the Dirac equation with equal mixture of vector and scalar potentials. Several particular cases such as the ring-shaped non-spherical harmonic oscillator, the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed. 相似文献
8.
将Ermakov系统加以推广,得出受到与速度平方成正比的力的变频率谐振子的不变量,求出其普遍解. 相似文献
9.
The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. 相似文献
10.
We construct here the coherent states (annihilation operator eigenstates) of a damped harmonic oscillator. These coherent
states, which are normalizable, have the desired behaviour in the classical limit (ℏ→0). 相似文献
11.
受与速度平方成正比的力的变频率谐振子(THOFQV)可以用一个适当的Lagrangian量来描述,可以求出THOFQV的普遍解.再利用不变量算子求解该系统的Schrdinger方程,得到本征函数和本征值.
关键词:
谐振子
不变量
本征函数
本征值 相似文献
12.
本文用不变本征算符方法研究非对易相空间中三模坐标动量耦合谐振子的能谱,分别得到了非耦合和坐标动量耦合两种情况下谐振子能谱的解析解,其中包括受非对易参数θ和φ影响的解λ0,1和λ1,1,以及不受非对易参数θ和φ影响的解λ0,2和λ1,2.然后,分析了两类耦合参数κ和η对三模坐标动量耦合谐振子能谱的影响.结果发现,耦合参数κ和η对λ1,1的影响是相同的,且当κ=η时,耦合系数κ和η对λ1,1是没有影响的. 相似文献
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A universal practical formula is given for calculating an integral which includes two confluent hypergeometric functions, power and exponential functions; then by means of this formula, the expressions of the radial matrix elements for a relativistic harmonic oscillator are given. 相似文献
15.
Jeong Ryeol Choi 《Pramana》2004,62(1):13-29
By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator.
The coherent states, both inx- andp-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger thankh/2 and is equal to the minimum of the uncertainty product of the number states. The displaced wave packet for Caldirola-Kanai
oscillator in coherent state oscillates back and forth with time about the center as for a classical oscillator. The amplitude
of oscillation with no driving force decreases due to the dissipation in the system. However, the oscillation with resonant
frequency oscillates with a large amplitude, even after a sufficient time elapse. 相似文献
16.
研究了由交叉相关高斯白噪声驱动的过阻尼谐振子的随机共振,其中加法噪声被周期信号所调制,运用平稳关联函数的傅里叶变换,导出了过阻尼谐振子随机模型信噪比的精确表达式.结果揭示:在过阻尼谐振子的随机模型中存在二类随机共振.一类随机共振表现为信噪比随乘法噪声强度Q变化的曲线存在共振峰,另一类随机共振表现为信噪比随振子频率ω变化的曲线存在共振峰.大幅度改变信号频率Ω值的大小,信噪比随乘法噪声强度Q变化的曲线有单峰,一峰一谷和单调变化三种不同的形式. 相似文献
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采用新的方法,推导出三维各向同性谐振子径向基本算符r,r,1r对本征函数的作用结果,由此得出其升降算符及其他新的公式,并证明文献[1]中的结论有误
关键词:
基本算符 升降算符 三维谐振子 相似文献
19.
从量子-经典轨道和几何相两方面, 研究了二维旋转平移谐振子系统的量子-经典对应. 通过广义规范变换得到了Lissajous经典周期轨道和Hannay角. 另外, 使用含时规范变换解析推导了旋转平移谐振子系统Schrödinger方程的本征波函数和Berry相, 得出结论: 原规范中的非绝热Berry相是经典Hannay角的-n倍. 最后, 使用SU(2)自旋相干态叠加, 构造一稳态波函数, 其波函数的概率云很好地局域于经典轨道上, 满足几何相位和经典轨道同时对应. 相似文献