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

Click For Summary
SUMMARY

The discussion centers on the approximation of each quantum oscillator's energy as kT at low temperatures, specifically addressing the excitation of vibration modes where hω < kT. At these temperatures, only certain modes are significantly excited, leading to a classical approximation of energy. The average energy of these modes aligns closely with kT, despite the quantum nature of the oscillators, due to the probability distribution of excitations. The relationship between average energy at temperature T and zero temperature is defined as ⟨E⟩_T - ⟨E⟩_0 ≈ kT.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly quantum oscillators.
  • Familiarity with statistical mechanics concepts, including the Boltzmann distribution.
  • Knowledge of thermodynamic temperature and its relation to energy.
  • Basic grasp of classical mechanics and its approximation in quantum systems.
NEXT STEPS
  • Study the Boltzmann distribution and its implications in statistical mechanics.
  • Explore the concept of quantum harmonic oscillators and their energy levels.
  • Learn about the classical limit of quantum systems and when it applies.
  • Investigate the relationship between temperature and energy in thermodynamic systems.
USEFUL FOR

Students and researchers in physics, particularly those focusing on quantum mechanics, statistical mechanics, and thermodynamics, will benefit from this discussion.

aaaa202
Messages
1,144
Reaction score
2
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?
 
Physics news on Phys.org
What is meant that ##\langle E \rangle_T-\langle E \rangle_0\approx kT##
 

Similar threads

Undergrad Cyclotron resonance and Landau Levels
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Questions on Debye's Model of solids
  • · Replies 1 ·
Replies
1
Views
2K
Thermal Physics: Photon Statistics on Bose Particles
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Why Is Average Energy per Mode in Rayleigh-Jeans Law Always kT?
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Why does superconductivity occur?
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad Atom as a harmonic oscillator of radition
  • · Replies 14 ·
Replies
14
Views
3K
Vibrational energy at low temperatures
  • · Replies 1 ·
Replies
1
Views
2K
Quantum Harmonic Oscillator - What is the Temperature of the system?
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Classical Limit of a Quantum Harmonic Oscillator
  • · Replies 1 ·
Replies
1
Views
2K
Admissions Could I please get critique on my SOP? (Experimental Biophysics)
  • · Replies 9 ·
Replies
9
Views
2K