We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-z...

Unlike its classical counterpart, the ground state of a quantum harmonic oscillator yields a non-zero value which has led to a significant problem regarding the cosmological constant. We will show that since observables, including that of energy, serve as a reference frame for an observer, not only is the harmonic oscillator fluctuating at the ground level, so is the reference frame of the obse...

The main result of this article gives scaling asymptotics the Wigner distributions $W_{\varphi_N^{\gamma},\varphi_N^{\gamma}}$ isotropic harmonic oscillator orbital coherent states $\varphi_N^{\gamma}$ concentrating along Hamiltonian orbits $\gamma$ in shrinking tubes around phase space. In particular, these exhibit a $\textit{hybrid}$ semi-classical scaling. That is, simultaneously, we have an...

We present the path integral formulation of quantum mechanics and demonstrate its equivalence to the Schrödinger picture. We apply the method to the free particle and quantum harmonic oscillator, investigate the Euclidean path integral, and discuss other applications.

We propose a new method to calculate expectation values of a delta function of the Hamiltonian, Ψ | δ(ˆ H − E) | Ψ. Since the delta function can be replaced with a Gaussian function, we evaluate Ψ | β π e −β(ˆ H−E) 2 | Ψ with large β adopting the Suzuki-Trotter decomposition. Errors of the approximate calculations with the finite Trotter number N t are estimated to be O(1/N K t) for the Kth-ord...

Abstract. The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the LeviCivita transformation. These connections lead to an approach to solve the Coulomb problems using the results of the harmonic oscillator potential in the above...

The d-dimensional generalization of the point canonical transformation for a quantum particle endowed with a position-dependent mass in Schrödinger equation is described. Illustrative examples including; the harmonic oscillator, Coulomb, spiked harmonic, Kratzer, Morse oscillator, Pőschl-Teller and Hulthén potentials are used as reference potentials to obtain exact energy eigenvalues and eigenf...

The fermionic oscillator defined by the algebraic relations cc∗ + c∗c = 1 and c = 0 admits the homogeneous group O(2) as its invariance group. We show that, the structure of the inhomogeneous invariance group of this oscillator is a quantum group. Quantum field theory which describes the ultimate behavior of elementary particles and fields in physics fundamentally depends on the concepts of the...

We present an interesting result regarding the implication of truncating the wavepacket of the harmonic oscillator. We show that disregarding the non-significant tails of a function which is the superposition of eigenfunctions of the harmonic oscillator has a remarkable consequence. Namely, there exit infinitely many different superpositions giving rise to the same function on the interval. Uni...

Multiparametric quantum gl(2) algebras are presented according to a classification based on their corresponding Lie bialgebra structures. From them, the non-relativistic limit leading to quantum harmonic oscillator algebras is implemented in the form of generalized Lie bialgebra contractions.