(a) Describe the energy levels of the system. (b) Express the creation and annihilation operator in their representation in Cartesian coordinates. (c) Use the creation and annihilation operators to derive the 2 eigenfunctions with lower energies.

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Charged oscillator. Consider a one-dimensional particle of mass m subjected to the potential of a
harmonic oscillator. However, additionally that particle has a charge q such that it moves in a
constant electric field E. Therefore, this system is subject to an effective potential
1
V (£) =mwx? – qEX
(a) Describe the energy levels of the system.
(b) Express the creation and annihilation operator in their representation in Cartesian coordinates.
(c) Use the creation and annihilation operators to derive the 2 eigenfunctions with lower energies.
Transcribed Image Text:Charged oscillator. Consider a one-dimensional particle of mass m subjected to the potential of a harmonic oscillator. However, additionally that particle has a charge q such that it moves in a constant electric field E. Therefore, this system is subject to an effective potential 1 V (£) =mwx? – qEX (a) Describe the energy levels of the system. (b) Express the creation and annihilation operator in their representation in Cartesian coordinates. (c) Use the creation and annihilation operators to derive the 2 eigenfunctions with lower energies.
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