EMERGING TRENDS IN COMPUTING
QUANTUM COMPUTING
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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In the 1D quantum harmonic oscillator, the momentum operator p provides a nonzero matrix element ____
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between any two energy eigenstates
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only between the ground state and the first excited state
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only between nearest-neighbour energy eigenstates
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none of the others
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Explanation:
Detailed explanation-1: -We know from our experience with classical mechanics that a particle of mass m subject to a linear restoring force F(x) = −x, where x is the force constant, results in one-dimensional simple harmonic motion with an oscillation frequency. w = √K/m.
Detailed explanation-2: -Zero Point Energy Unlike a classical oscillator where the lowest vibrational energy is zero (with the oscillator having zero momentum or kinetic energy) the quantum mechanical oscillator has a minimum energy for v = 0 of E0 = (1/2) hw/2p. This is known as the Zero Point Energy of the oscillator.
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