Derivation of number of quantum states

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SUMMARY

The derivation of the number of quantum states (QS) from classical states (CS) is defined by the equations #CS = V_spatial * V_momentum and #QS = #CS/h, where h represents Planck's constant. This relationship illustrates how classical mechanics transitions into quantum mechanics by quantifying the states available in a given system. Understanding this derivation is crucial for grasping the foundational concepts of quantum mechanics and its implications in various physical systems.

PREREQUISITES
  • Familiarity with classical mechanics concepts, particularly volume in phase space.
  • Understanding of quantum mechanics fundamentals, including the significance of Planck's constant.
  • Basic knowledge of statistical mechanics and its application to quantum systems.
  • Experience with mathematical derivations involving integrals and limits.
NEXT STEPS
  • Study the derivation of phase space volume in classical mechanics.
  • Research the implications of Planck's constant in quantum mechanics.
  • Explore statistical mechanics and its role in quantum state calculations.
  • Learn about the transition from classical to quantum systems in physics.
USEFUL FOR

Students and researchers in physics, particularly those focusing on quantum mechanics, as well as educators seeking to explain the relationship between classical and quantum states.

TheCanadian
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Hi,

I recently saw a derivation that included:

[1] #CS = V_spatial * V_momentum

[2] #QS = #CS/h

(where # indicates it's the total number of the variable)

quantum states = QS; classical states = CS; h is Planck's constant

If possible, do you mind explaining or directing me to references that explain how [2] is derived and makes sense?
 
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TheCanadian said:
I recently saw a derivation
Where?
 

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