A laboratory oscillator consists of a mass of 1 gram on aspring. The mass is dis

Question

A laboratory oscillator consists of a mass of 1 gram on aspring. The mass is displaced from its equilibirum position andreleased. The oscillator exhibits a period of 1 second and the masspasses through the zero displacement position with a velocity of 10cm/sec. The subpart of this question that I'm having trouble withis: Is this oscillator probably in an eigenstate of theHamiltonian? I don't know whether this is just a conceptual question orwhether the answer can actually be determined from the givenvalues. A laboratory oscillator consists of a mass of 1 gram on aspring. The mass is displaced from its equilibirum position andreleased. The oscillator exhibits a period of 1 second and the masspasses through the zero displacement position with a velocity of 10cm/sec. The subpart of this question that I'm having trouble withis: Is this oscillator probably in an eigenstate of theHamiltonian? I don't know whether this is just a conceptual question orwhether the answer can actually be determined from the givenvalues.

Explanation / Answer

Since the mass and velocity are not small, the problem isessentially classical. From a quantum point of view, the energy level (associated with theclassical total energy) is extremely high, say, N where N is a verylarge number. Also, quantum mechanically, the motion is describedby a wave packet of finite spread in the x-space. That translatesto the fact that the wave packet is a superposition of many energyeigenstates with quantum numbers in a range around N. So, bottomline: no, the oscillator is not in a strict energy eigenstate ofthe hamiltonian. hope this helps!

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