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We have 4 results for Harmonic oscillator.
1 Citation This is a very significant physical result because it tells us that the energy of a system described by a harmonic oscillator potential cannot have zero energy. Physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature. The energy of the ground vibrational state is often referred to as "zero point vibration". The zero point energy is sufficient to prevent liquid helium-4 from freezing at atmospheric pressure, n, technorati.com
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1 Citation Classically, a one-dimensional harmonic oscillator is a system with a mass under a restoring force proportional to displacement from the equilibrium position: F =- kx . The energy is , and the equation of motion has solution , where . Analogously, a one-dimensional quantum harmonic oscillator is a particle with Hamiltonian , where here p is the quantum momentum operator, and x the position operator. In the position basis, this is then . A cursory examination of the expectation, technorati.com
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1 Citation In a previous Friday post , I demonstrated one method of determining the energy eigenvalues for the one-dimensional quantum harmonic oscillator. In particular, we took the (time-independent) Schrödinger equation , and by defining dimensionless parameters , , and then attempting a solution of the form , we derived the differential equation , where the series solution has recursion relation . Then, the requirement that the wavefunction be normalizable requires that the series solution t, technorati.com
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1 Citation Let us consider the isotropic three-dimensional quantum harmonic oscillator: we have (where the particle mass is now m 0 to prevent confusion later). In cartesian coordinates, this becomes: where H x , H y , and H z are each the hamiltonian for a one-dimensional harmonic oscillator, in the x, y, and z directions respectively. Thus, the energy eigenstates will be products of eigenstates of these three; we have energy levels . Thus, we have energies , with degeneracy equal to t, technorati.com
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