2.32 Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by V(x,y) = kx² + k,y². (a) Write down the expression for the hamiltonian operator for such a system. (b) What is the general expression for the allowable energy levels of the two-dimensional harmonic oscillator? (c) What is the energy of the ground state (the lowest energy state)? Hint. The hamiltonian operator can be written as a sum of operators.
2.32 Consider a harmonic oscillator of mass m undergoing harmonic motion in two dimensions x and y. The potential energy is given by V(x,y) = kx² + k,y². (a) Write down the expression for the hamiltonian operator for such a system. (b) What is the general expression for the allowable energy levels of the two-dimensional harmonic oscillator? (c) What is the energy of the ground state (the lowest energy state)? Hint. The hamiltonian operator can be written as a sum of operators.
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Transcribed Image Text:2.32 Consider a harmonic oscillator of mass m undergoing
harmonic motion in two dimensions x and y. The potential
energy is given by V(x,y) = kx² + k,y². (a) Write down the
expression for the hamiltonian operator for such a system.
(b) What is the general expression for the allowable energy
levels of the two-dimensional harmonic oscillator? (c) What
is the energy of the ground state (the lowest energy state)?
Hint. The hamiltonian operator can be written as a sum
of operators.
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