# Superposition state

## Main Question or Discussion Point

Structure and dynamics in the microcosm are inherently connected by the laws of quantum mechanics.
Take, for example, a particle put in a superposition of its
ground state
0
x of energy W 0
and the first excited
state
1
x of energy W 1
. Such a superposition state is
referred to as a wave packet. Change in the position of
its center of mass is the closest quantum mechanical ana-log of classical motion. Solution of the Schrödinger
equation for the particle’s wave function x yields an
oscillatory motion with the oscillation period T
osc
=2 / W , where W = W 1
− W 0
. The larger the energy
separation W between the two eigenstates, the faster is
the particle’s motion in the superposition state.
would you please explain why?

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## Answers and Replies

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Jano L.
Gold Member
The larger the energy
separation W between the two eigenstates, the faster is
the particle’s motion in the superposition state.
The oscillation of the wave function is faster, but whether the individual particle moves faster is not so clear. Why do you think so?

If you want to google "quantum beats" you'll find all sorts of careful examples with useful pictures to help understand it. To understand what's going on with "speed" or the particle, use the fourier transform to look at the momentum-space wave function rather than the position space one.

If you want to google "quantum beats" you'll find all sorts of careful examples with useful pictures to help understand it. To understand what's going on with "speed" or the particle, use the fourier transform to look at the momentum-space wave function rather than the position space one.