Why Is Each Quantum Oscillator's Energy Approximated as kT at Low Temperatures?

In summary, the last sentence of the conversation is discussing the excitation of vibration modes at low temperatures. It states that the excitation of these modes will be approximately classical, meaning they will follow classical mechanics principles. Each mode will have an energy close to kT, which is the energy associated with thermal motion at a given temperature. This energy is determined by a probability distribution and can be approximated by the difference between the average energy at temperature T and the average energy at temperature 0.
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Just one short question about something I didn't understand in my book: "At low temperaturs only vibration modes where hω<kT will be excited to any appreciable extent. The excitation of these modes will be approimately classical each with an energy close to kT."
I don't understand the last sentence. What is meant by a classical exciation? The energy of the modes will be (n+½)hω for which there is a probability distribution - on this ground how can you say that the energy of each excitation is approx kT?
 
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  • #2
What is meant that ##\langle E \rangle_T-\langle E \rangle_0\approx kT##
 

Related to Why Is Each Quantum Oscillator's Energy Approximated as kT at Low Temperatures?

1. What is a quantum oscillator?

A quantum oscillator is a physical system that exhibits periodic motion and follows the laws of quantum mechanics. Examples include atoms, molecules, and subatomic particles.

2. What is the significance of quantum oscillator statistics?

Quantum oscillator statistics are important because they describe the probability distribution of the energy levels of a quantum oscillator, which is essential for understanding the behavior and properties of many physical systems.

3. How are quantum oscillator statistics different from classical statistics?

Classical statistics describe the behavior of macroscopic objects with many particles, while quantum oscillator statistics describe the behavior of individual particles at the microscopic level. Classical statistics follow the laws of classical mechanics, while quantum oscillator statistics follow the laws of quantum mechanics.

4. What is the difference between Bose-Einstein and Fermi-Dirac statistics for quantum oscillators?

Bose-Einstein statistics apply to quantum oscillators with integer spin, such as photons and phonons, and allow multiple particles to occupy the same energy level. Fermi-Dirac statistics apply to quantum oscillators with half-integer spin, such as electrons, and do not allow multiple particles to occupy the same energy level.

5. How do quantum oscillator statistics affect the properties of materials?

Quantum oscillator statistics play a crucial role in determining the electronic, thermal, and magnetic properties of materials. For example, the difference between Bose-Einstein and Fermi-Dirac statistics can explain the difference between conductors, insulators, and semiconductors.

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