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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

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A Mathematical Analysis of the Harmonic Oscillator in Quantum Mechanics

Solarz, Philip January 2021 (has links)
In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. We also classify the inverse to the Hamiltonian operator as a Schatten-von Neumann operator. Finally, we derive the fundamental solution to the Schrödinger Equation corresponding to the Harmonic Oscillator using Mehler’s formula.
Functional Analysis
Quantum Mechanics
Harmonic Oscillator
Schrödinger Equation
Hamiltonian Operator
Hermite Functions
Hilbert Space
Schatten-von Neumann Operator
Mehler's Formula
Mathematical Analysis
Matematisk analys

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