Solutions to quantum harmonic oscillator
[DOC File]St. John's University Unofficial faculty Main Page
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Here we analyze a system of great importance in physics, the quantum mechanical harmonic oscillator. The physics and mathematics of the oscillator are relevant to the emission and absorption of light by matter (blackbody radiation), the analyses of radiation and fields, the treatment of systems of identical particles, and other basic problems.
[DOC File]University of Manchester
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Solutions can be found by a complicated argument similar to the one for the Harmonic oscillator, but (without proof) we have (11.17) and (11.18) The explicit, and normalised, forms of a few of these states are
[DOC File]Quantum Basis for Quantum Computing - vlsicad page
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The linear harmonic oscillator is a model that in fact serves as an approximation to many critical phenomena, though in general not quantum computing (The reason is that the linear harmonic oscillator is linear to all orders in the presence of a driving force. The basic quantum logic device must be highly nonlinear as seen below).
[DOC File]1 - comedia
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To solve the problem of time evolution of a state of a quantum harmonic oscillator we used the time dependent Schrödinger equation which is a differential equation. We discussed this Schrödinger equation in position space and saw that general solutions are given by linear combination of the eigenvalues.
[DOC File]2 - Colby College
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The energies (eigenvalues) of the one-dimensional harmonic oscillator may be found from the relations. Combining these, we obtain. Unlike the corresponding classical result, we find that the quantum mechanical energy is quantized, in units of , where ω is the classical frequency ω2 = k/m. v is called the vibrational quantum number.
[DOC File]Chemistry 372 - University of Babylon
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The harmonic oscillator approximation can also be evaluated using quantum mechanics. The quantum mechanical solution to the Schrödinger equation for a harmonic oscillator gives a series of quantized energies with the following solutions: Evib = hν0(v + ½) (v = 0, 1, 2, …) (4) where v is the vibrational quantum number and. ν0 = ½π (k/m ...
[DOC File]Chemistry 372 - Personal Websites | Personal Websites
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The quantum mechanical solution to the Schrödinger equation for a harmonic oscillator gives a series of quantized energies with the following solutions: Evib = hν0(v + ½) (v = 0, 1, 2, …) (4) where v is the vibrational quantum number and
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