Qian Shang-Wu

Supersymmetry and Shape Invariance of Hartmann Potential and Ring-Shaped Oscillator Potential in the r and θ Dimensions of Spherical Polar Coordinates

This article shows that in spherical polar coordinates, some noncentral separable potentials have supersymmetry and shape invariance in the r and θ dimensions, we choose Hartmann potential and ring-shaped oscillator as two important examples, thus in principle the energy eigenvalues and energy eigenfunctions of such the potentials in the r and θ dimensions can be obtained by the method of supersymmetric quantum mechanics. Here we use an alternative method to get the required results.

Gauge Invariance of a Time-Dependent Harmonic Oscillator in Magnetic Dipole Approximation

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.

Separability of Pure and Mixed States of the Quantum Network of Four Nodes

This article discusses the separability of the pure and mixed states of the quantum network of four nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.

Correspondence Between GHZ States and Oriented Links in Knot Theory

This article generalizes our previous results for a quantum system of two nodes to a quantum system of nodes. It shows that there is a one to one correspondence between states for a quantum system of nodes and oriented links of the linkage N1 in knot theory, where is the number of crossings of the link with m components, the subscript 1 denotes the order of the unoriented m components link with N crossings, i.e. the first type, actually the simplest type.

Correspondence Between Bell Bases and Oriented Links in Knot Theory

From the comparison of correlation tensor in the theory of quantum network, the Alexander relation matrix in the theory of knot crystals and the identical inversion relations under the action of Pauli matrices, we show that there is a one to one correspondence between four Bell bases and four oriented links of the linkage in knot theory.

Metric of Rotating Charged Spherical Mass in Vacuum for Vector Graviton Metric Theory of Gravitation

Based on the vector graviton metric theory of gravitation (VGM) suggested by one of the authors of this article, using the method of null tetrad and analytic continuation, this paper gives the metric of the rotating charged spherical mass in VGM. The result shows once again that a replacement of G by G* = G(1 − GM/2r) in general relativity will yield the corresponding result in VGM for the metric in vacuum.

Knotted Picture of a Quantum Network of Two Nodes

This article discusses the variation of the knotted picture of the quantum pure state with the variation of the complex coefficients α and β. It is shown that there are three kinds of link that correspond to three different ranks of the matrix of covariance correlation tensor, i.e., the zero rank corresponds to trivial link, the rank one corresponds to the two-component link with two crossings, and the rank three corresponds to the two-component link with four crossings.

Knotted Picture of Degree of Entanglement of Quantum Pure State of Two Nodes |χ〉 = α|↑↓〉 + β|↓↑〉

From the knotted pictures this article gives a possible quantitative measure of the degree of entanglement. We suggest to use the area ratio to measure the degree of entanglement, moreover, from the two parts of the non-overlapping area we can also know vividly and pictorially the phase difference between the two variable coefficients α and β.

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of two nodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum network theory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor is equal to zero for all possible and .

Criterion of Quantum Entanglement and the Covariance Correlation Tensor in the Theory of Quantum Network

This article discusses the covariance correlation tensor (CCT) in quantum network theory for four Bell bases in detail. Furthermore, it gives the expression of the density operator in terms of CCT for a quantum network of three nodes, thus gives the criterion of entanglement for this case, i.e. the conditions of complete separability and partial separability for a given quantum state of three bodies. Finally it discusses the general case for the quantum network of nodes.