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111.
The improved quantization rule simplifies the calculation of the energy levels for the exactly solvable quantum system. In this Letter we calculate the energy levels of the Schrödinger equation with the symmetric and asymmetric trigonometric Rosen-Morse potentials by the improved quantization rule. 相似文献
112.
We propose a new method to transform a pixel image to the corresponding quantum-pixel using a qubit per pixel to represent each pixels classical weight in a quantum image matrix weight. All qubits are linear superposition, changing the coefficients level by level to the entire longitude of the gray scale with respect to the base states of the qubit. Classically, these states are just bytes represented in a binary matrix, having code combinations of 1 or 0 at all pixel locations. This method introduces a qubit-pixel image representation of images captured by classical optoelectronic methods. 相似文献
113.
The associated Legendre polynomials play an important role in the central fields, but in the case of the non-central field we have to introduce the universal associated Legendre polynomials Pl'm'(x) when studying the modified Pschl-Teller potential and the single ring-shaped potential. We present the evaluations of the integrals involving the universal associated Legendre polynomials and the factor (1-x2)-p-1 as well as some important byproducts of this integral which are useful in deriving the matrix elements in spin-orbit interaction. The calculations are obtained systematically using some properties of the generalized hypergeometric series. 相似文献
114.
We first introduce the universal associated Legendre polynomials, which are occurred in studying the non-central fields such as the single ring-shaped potential and then present definite integrals IA±(a, τ)=∫-1+1xa[Pl'm'(x)]2/(1±x)τdx, a=0, 1, 2, 3, 4, 5, 6, τ=1, 2, 3, IB(b, σ)=∫-1+1xb[Pl'm'(x)]2/(1- x2)σdx, b=0, 2, 4, 6, 8, σ=1, 2, 3, and IC±(c, κ)=∫-1+1xc[Pl'm'(x)]2/[(1-x2)κ(1±x)]dx, c=0, 1, 2, 3, 4, 5, 6, 7, 8, κ=1, 2. The superindices “±” in IA±(a, τ) and IC±(c, κ) correspond to those of the factor (1±x) involved in weight functions. The formulas obtained in this work and also those for integer quantum numbers l' and m' are very useful and unavailable in classic handbooks. 相似文献
115.
Ariadna J. Torres-Arenas Qian Dong Guo-Hua Sun Shi-Hai Dong 《Physics letters. A》2018,382(26):1752-1759
We show how the product of the radial position and momentum uncertainties can be obtained analytically for the infinite circular well potential. Some interesting features are found. First, the uncertainty Δr increases with the radius R and the quantum number n, the n-th root of the Bessel function. The variation of the Δr is almost independent of the quantum number n for and it will arrive to a constant for a large n, say . Second, we find that the relative dispersion is independent of the radius R. Moreover, the relative dispersion increases with the quantum number n but decreases with the azimuthal quantum number m. Third, the momentum uncertainty Δp decreases with the radius R and increases with the quantum numbers and n. Fourth, the product of the position-momentum uncertainty relations is independent of the radius R and increases with the quantum numbers m and n. Finally, we present the analytical expression for the Fisher entropy. Notice that the Fisher entropy decreases with the radius R and it increases with the quantum numbers and n. Also, we find that the Cramer–Rao uncertainty relation is satisfied and it increases with the quantum numbers and n, too. 相似文献
116.
软骨凹顶藻Laurencia Cartilaginea 甾醇成分的研究 总被引:2,自引:0,他引:2
从中国南海软骨凹顶藻乙醇浸提物的乙酸乙酯相中 ,首次分离得到一种环二氧麦角甾醇 :5α,8α-环二氧麦角甾 - 6 ,2 2 -二烯 - 3β-醇 (1)。通过 GC- MS方法检测到了其他 5种甾醇化合物 :5 ,8-环二氧麦角甾 - 1,6 ,2 2 -三烯 - 3-醇 (2 ) ,麦角甾 - 6 ,2 2 -二烯 - 5 ,8-二羟基 - 3-酮 (3) ,豆甾 - 6 ,2 2 -二烯 - 5 ,8-二羟基 - 3-酮 (4) ,麦角甾 -5 ,7,9(11) ,2 2 -四烯 - 3-醇 (5 )以及豆甾 - 5 ,7,2 2 -三烯 - 3-醇 (6 ) 相似文献
117.
The momentum representation of the Morse potential is presented analytically by hypergeometric function. The properties with respect to the momentum p and potential parameter β are studied. Note that |Ψ(p)| is a nodeless function and the mutual orthogonality of functions is ensured by the phase functions arg[Ψ(p)]. It is interesting to see that the |Ψ(p)| is symmetric with respect to the axis p=0 and the number of wave crest of |Ψ(p)| is equal to n+1. We also study the variation of |Ψ(p)| with respect to β. The amplitude of |Ψ(p)| first increases with the quantum number n and then deceases. Finally, we notice that the discontinuity in phase occurs at some points of the momentum p and the position and momentum probability densities are symmetric with respect to their arguments. 相似文献
118.
Qian Dong Ariadna J. Torres-Arenas Guo-Hua Sun Wen-Chao Qiang Shi-Hai Dong 《Frontiers of Physics》2019,14(2):21603
In this work we analyze the characteristics of quantum entanglement of the Dirac field in noninertial reference frames in the context of a new type pseudo-pure state, which is composed of the Bell states. This will help us to understand the relationship between the relativity and quantum information theory. Some states will be changed from entangled states into separable ones around the critical value F = 1/4, but there is no such a critical value for the variable y related to acceleration a. We find that the negativity NABI (ρTAABI) increases with F but decreases with the variable y, while the variation of the negativity NBIBII(ρTAABI) is opposite to that of the negativity NABI (ρTAABI). We also study the von Neumann entropies S(ρABI) and S(ρBIBII). We find that the S(ρABI) increases with variable y but S(ρBIBII) is independent of it. However, both S(ρABI) and S(ρBIBII) first decreases with F and then increases with it. The concurrences C(ρABI) and C(ρBIBII) are also discussed. We find that the former decreases with y while the latter increases with y but both of them first increase with F and then decrease with it. 相似文献
119.
The bound state solutions of the Klein-Gordon equation with the rotating Deng-Fan molecular potential are presented by using a proper approximation to the centrifugal term within the framework of equal scalar and vector Deng-Fan potentials. It is shown that the solutions can be expressed by the generalized hypergeometric functions. The normalized wavefunctions are also derived. 相似文献
120.
In this work we study the quantum system with the symmetric Konwent potential and show how to find its exact solutions. We find that the solutions are given by the confluent Heun function. The eigenvalues have to be calculated numerically because series expansion method does not work due to the variable z ≥ 1. The properties of the wave functions depending on the potential parameter A are illustrated for given potential parameters V_0 and a. The wave functions are shrunk towards the origin with the increasing |A|. In particular, the amplitude of wave function of the second excited state moves towards the origin when the positive parameter A decreases. We notice that the energy levels ε_i increase with the increasing potential parameter |A| ≥ 1, but the variation of the energy levels becomes complicated for |A| ∈(0, 1), which possesses a double well. It is seen that the energy levels ε_i increase with |A| for the parameter interval A ∈(-1, 0), while they decrease with |A| for the parameter interval A ∈(0, 1). 相似文献