相关论文: Exact bound states in volcano potentials
Classical mechanics involves position and momentum variables that must be special coordinates chosen to promote to suitable quantum operators. Since classical variables may be broadly chosen, only unique variables should be chosen. We will…
An exact quantization rule for the Schr\"{o}dinger equation is presented. In the exact quantization rule, in addition to $N\pi$, there is an integral term, called the quantum correction. For the exactly solvable systems we find that the…
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…
The finite square potential well is a staple problem in introductory quantum mechanics. There is an extensive literature on the determination of the allowed energies, which requires the solution of a transcendental equation by numerical,…
The quantum statistical mechanics of an ideal gas with a general free-particle energy obeying fractional exclusion statistics are systematically investigated in arbitrary dimensions. The pressure relations, the relation between pressure and…
We consider an elliptic pseudo differential equation in a multi-dimensional cone and starting wave factorization concept we add some boundary conditions. For the simplest cases explicit formulas for solution are given like layer potentials…
The uncertainty associated with probing the quantum state is expressed as the effective abundance (measure) of possibilities for its collapse. New kinds of uncertainty limits entailed by quantum description of the physical system arise in…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
The imposition of boundary conditions upon a quantized field can lead to singular energy densities on the boundary. We treat the boundaries as quantum mechanical objects with a nonzero position uncertainty, and show that the singular energy…
We derive analytic expressions of the recursive solutions to the Schr\"{o}dinger's equation by means of a cutoff potential technique for one-dimensional piecewise constant potentials. These solutions provide a method for accurately…
In modern fundamental theories there is consideration of higher dimensions, often in the context of what can be written as a Schr\"odinger equation. Thus, the energetics of bound states in different dimensions is of interest. By considering…
The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time in which to perform the measurement. This paper considers the possibility that $\Delta E$, the uncertainty in the energy, may be…
For zero energy, $E=0$, we derive exact, classical and quantum solutions for {\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$, $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions…
In a large class of factorizing scattering models, we construct candidates for the local energy density on the one-particle level starting from first principles, namely from the abstract properties of the energy density. We find that the…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
Bound states of hyperbolic potential is investigated by means of a generalized pseudospectral method. Significantly improved eigenvalues, eigenfunctions are obtained efficiently for arbitrary $n, \ell$ quantum states by solving the relevant…
A set of exactly solvable one-dimensional quantum mechanical potentials is described. It is defined by a finite-difference-differential equation generating in the limiting cases the Rosen-Morse, harmonic, and P\"oschl-Teller potentials.…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…