Related papers: Morse potential derived from first principles
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
We show that the energy of a perturbed system can be fully recovered from the unperturbed system's electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule and…
Quantizing the transfer of energy and momentum between interacting particles, we obtain a quantum impulse equation and relations that the corresponding mechanical power, force and torque satisfy. In addition to the energy-frequency and…
A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it…
In this work we explore a generalization of the Dirac and Klein-Gordon (KG) oscillators, provided with a deformed linear momentum inspired in nonextensive statistics, that gives place to the Morse potential in relativistic contexts by first…
In this paper Quantum Mechanics with Fundamental Length is chosen as the theory for describing the early Universe. This is possible due to the presence in the theory of General Uncertainty Relations from which unavoidable it follows that in…
The correspondence of a new form of quantum mechanics based on a quantum version of the action principle, which was proposed earlier [arXiv:0807.3508], with the ordinary quantum mechanics is established. New potentialities of the quantum…
The minimal-length paradigm is a cornerstone of quantum gravity phenomenology. Recently, it has been demonstrated that minimal-length quantum mechanics can alternatively be described as an undeformed theory set on a nontrivial momentum…
Methodologies for creating reactive potential energy surfaces from molecular mechanics force-fields are becoming increasingly popular. To date, molecular mechanics force-fields use harmonic expressions to treat bonding stretches, which is a…
By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the…
We model the Hartree-exchange-correlation potential of Kohn-Sham density-functional theory adopting a novel strategy inspired by the strictly-correlated-electrons limit and relying on the exact decomposition of the potential based on the…
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are…
We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment…
We review the essentials of the formalism of quantum mechanics based on a deformed Heisenbeg algebra, leading to the existence of a minimal length scale. We compute in this context, the energy spectra of the pseudoharmonic oscillator and…
Supersymmetric quantum mechanics is a powerful tool for generating exactly solvable potentials departing from a given initial one. In this article the first- and second- order supersymmetric transformations will be used to obtain new…
We present new aspects of the electromagnetic field by introducting the natural potentials. These natural potentials are suitable for constructing the first order distortions of the metric tensor of Complex Relativity - the theory combining…
By factorization of the Hamiltonian describing the quantum mechanics of the continuous q-Hermite polynomial, the creation and annihilation operators of the q-oscillator are obtained. They satisfy a q-oscillator algebra as a consequence of…
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and…
Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a…
A minimal observable length is a common feature of theories that aim to merge quantum physics and gravity. Quantum mechanically, this concept is associated to a nonzero minimal uncertainty in position measurements, which is encoded in…