The variational method applied to the harmonic oscillator in the presence of a delta function potential

@article{Ghose2021TheVM,
  title={The variational method applied to the harmonic oscillator in the presence of a delta function potential},
  author={Indrajit Ghose and Parongama Sen},
  journal={European Journal of Physics},
  year={2021},
  volume={42}
}
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension, where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent hypergeometric functions in general. The eigenfunctions obtained exactly are difficult to visualise and hence, to gain more insight, one can attempt to use model wave functions which are explicitly and simply expressed. Here, we apply the variational method to verify… 

Analytical study of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by a spatially power-law potential Vper(x) = λxα

In this work, we present a rigorous mathematical scheme for the derivation of the sth-order perturbative corrections to the solution to a one-dimensional harmonic oscillator perturbed by the

Variational approach to the Schrödinger equation with a delta-function potential

We obtain accurate eigenvalues of the one-dimensional Schrödinger equation with a Hamiltonian of the form H g = H + gδ(x), where δ(x) is the Dirac delta function. We show that the well known

References

SHOWING 1-10 OF 21 REFERENCES

Solution of the quantum harmonic oscillator plus a delta-function potential at the origin: the oddness of its even-parity solutions

We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of

Bound States Energies of a Harmonic Oscillator Perturbed by Point Interactions

We determine explicitly the exact transcendental bound states energies equation for a one-dimensional harmonic oscillator perturbed by a single and a double point interactions via Green’s function

The Dirac oscillator in the presence of a chain of delta-function potentials

We study the spectroscopy of the one-dimensional Dirac oscillator perturbed by a chain of delta-shaped potentials. We consider two cases: scalar and vector couplings. The transfer matrix method is

The Hamiltonian of the harmonic oscillator with an attractive \delta ^{\prime} -interaction centred at the origin as approximated by the one with a triple of attractive \delta -interactions

In this note we provide an alternative way of defining the self-adjoint Hamiltonian of the harmonic oscillator perturbed by an attractive δ ′ ?> - interaction, of strength β ?> , centred at 0 (the

One-dimensional hydrogen atom

  • R. Loudon
  • Physics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2016
The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the

One-dimensional delta -potential in external fields

The 1D delta -potential with strength Omega in an external in-plane magnetic field B is considered theoretically. Energy dependences on Omega and d (with d being normalized to the magnetic radial

Harmonic oscillator with a δ-function potential

Harmonic oscillator with a δ-function potential is analysed and compact expressions are obtained for the energy eigenvalues of the even parity states. These energies tend to the energy eigenvalues of

An exact treatment of the Dirac delta function potential in the Schrödinger equation

This paper presents several cases in which the effects of the addition of a delta function potential on bound states can be computed exactly. In the case of the one dimensional Schrodinger equation,

One‐dimensional hydrogen molecule revisited

The energy of the one‐dimensional hydrogen molecule with δ‐function interactions between the particles is obtained using exact hydrogen molecule ion wave functions, a symmetrized product of hydrogen

Introduction to Quantum Mechanics

I. THEORY. 1. The Wave Function. 2. The Time-Independent Schrodinger Equation. 3. Formalism. 4. Quantum Mechanics in Three Dimensions. 5. Identical Particles. II. APPLICATIONS. 6. Time-Independent