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You may be familiar with several examples of harmonic oscillators form
classical mechanics, such as particles on a spring or the pendulum for small
deviation from equilibrium, etc.
Figure 7.1:
The mass on the spring and its equilibrium position
|
|
Let me look at the characteristics of one such example, a particle
of mass m on a spring. When the particle moves a distance x away from
the equilibrium position x0, there will be a restoring force
- kx pushing the particle back (x > 0 right of equilibrium, and
x < 0 on the left). This can be derived from a potential
V(x) = kx2. |
(7.1) |
Actually we shall write
k = m
. The equation of motion
m
= - m x |
(7.2) |
has the solution
x(t) = Acos( t) + Bsin( t). |
(7.3) |
We now consider how this system behaves quantum-mechanically.
Next: 7.1 Dimensionless coordinates
Up: Quantum Mechanics I
Previous: 6.3 Square barrier