Harmonic Oscillator: Energy Explained

Thread starter Abigale
Start date Apr 19, 2013
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Harmonic Harmonic oscillator Oscillator

In summary, a harmonic oscillator is a physical system with repetitive motion around a stable equilibrium point, described by a proportional restoring force. It stores energy in the form of potential energy when displaced, converting between potential and kinetic energy as it oscillates. The energy is directly proportional to the square of the amplitude and frequency, but can be lost through external forces resulting in a decrease in amplitude and total energy over time.

Apr 19, 2013

Abigale

Hi guys,

is there a reason why the energy of the harmonic oscillator is always written as:$$
E_{n} = \hbar \omega (n + \frac{1}{2})$$
instead of :
$$
E_{n} = h \nu (n + \frac{1}{2})$$
?

THX
Abby

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Apr 19, 2013

dextercioby

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It means the same, usually QM uses hbar to avoid the 2pi appearing everywhere.

1. What is a harmonic oscillator?

A harmonic oscillator is a physical system that has a repetitive motion around a stable equilibrium point. It can be described by a restoring force that is proportional to the displacement from the equilibrium point.

2. How does a harmonic oscillator store energy?

A harmonic oscillator stores energy in the form of potential energy when it is displaced from its equilibrium point. As it oscillates back and forth, the potential energy is converted into kinetic energy and vice versa.

3. What is the relationship between energy and amplitude in a harmonic oscillator?

The energy of a harmonic oscillator is directly proportional to the square of its amplitude. This means that a larger amplitude corresponds to a greater amount of energy stored in the oscillator.

4. Can a harmonic oscillator lose energy?

Yes, a harmonic oscillator can lose energy through various mechanisms such as friction or external forces. This results in a decrease in amplitude and a decrease in the total energy of the oscillator over time.

5. How is the energy of a harmonic oscillator related to its frequency?

The energy of a harmonic oscillator is directly proportional to its frequency. This means that a higher frequency corresponds to a greater amount of energy stored in the oscillator.