Related papers: Quantum mechanical bootstrap on the interval: obta…
We investigate non-relativistic quantum mechanical potentials between fermions generated by various classes of QFT operators and evaluate their singularity structure. These potentials can be generated either by four-fermion operators or by…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
We present in this paper a rather general method for the construction of so-called conditionally exactly solvable potentials. This method is based on algebraic tools known from supersymmetric quantum mechanics. Various families of…
Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…
A powerful method for calculating the eigenvalues of a Hamiltonian operator consists of converting the energy eigenvalue equation into a matrix equation by means of an appropriate basis set of functions. The convergence of the method can be…
In this paper, we consider the spectrum of a model in quantum electrodynamics with a spatial cutoff. It is proven that (1) the Hamiltonian is self-adjoint; (2) under the infrared regularity condition, the Hamiltonian has a unique ground…
We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
Quantum machine learning is considered one of the flagship applications of quantum computers, where variational quantum circuits could be the leading paradigm both in the near-term quantum devices and the early fault-tolerant quantum…
In this paper, we employ the bootstrap method, a technique that relies on consistency relations instead of direct diagonalization, to determine the expectation values in quantum many-body systems. We then use these values to assess the…
General positivity constraints linking various powers of observables in energy eigenstates can be used to sharply locate acceptable regions for the energy eigenvalues, provided that efficient recursive methods are available to calculate the…
We extend the notion of quasi-exactly solvable (QES) models from potential ones and differential equations to Bose systems. We obtain conditions under which algebraization of the part of the spectrum occurs. In some particular cases simple…
The bootstrap is a foundational tool in statistical inference, but its classical implementation relies on Monte Carlo resampling, introducing approximation error and incurring high computational cost -- especially for large datasets and…
Quantum-mechanical WKB-method is elaborated for the known quantum oscillator problem in curved 3-spaces models Euclid, Riemann, and Lobachevsky E_{3}, H_{3}, S_{3} in the framework of the complex variable function theory. Generalized…
A quantum finite multi-barrier system, with a periodic potential, is considered and exact expressions for its plane wave amplitudes are obtained using the Transfer Matrix method [10]. This quantum model is then associated with a stochastic…
Using extended Schwinger's quantization approach quantum mechanics on a Riemannian manifold $M$ with a given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally…
We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing…
A general non-commutative quantum mechanical system in a central potential $V=V(r)$ in two dimensions is considered. The spectrum is bounded from below and for large values of the anticommutative parameter $\theta $, we find an explicit…
Starting from the Hamiltonian formulation for the inhomogeneous Mixmaster dynam- ics, we approach its quantum features through the link of the quasi-classical limit. We fix the proper operator-ordering which ensures that the WKB continuity…