Wave-packet in configuration space

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SUMMARY

The discussion centers on the interpretation of wave packets in configuration space as described in Eugene P. Wigner's book "Group Theory and its Applications to the Quantum Mechanics of Atomic Spectra." It highlights the relationship between the classical motion of a system's point in multidimensional configuration space and the behavior of wave packets. The index of refraction for these waves is defined as ##\sqrt{2m(E-V)}\over E##, where ##E## is the total energy and ##V## is the potential energy. Understanding this relationship is crucial for interpreting quantum mechanics in a classical framework.

PREREQUISITES
  • Familiarity with quantum mechanics concepts, particularly wave packets
  • Understanding of configuration space in physics
  • Knowledge of classical mechanics and motion
  • Basic grasp of the principles of energy and potential energy in physics
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  • Study the derivation and implications of the index of refraction in quantum mechanics
  • Explore the concept of configuration space in greater detail
  • Learn about the mathematical formulation of wave packets in quantum mechanics
  • Investigate classical versus quantum descriptions of motion
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This discussion is beneficial for physicists, quantum mechanics students, and researchers interested in the intersection of classical and quantum theories, particularly those studying wave-packet behavior in configuration space.

Pradyuman
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In the book "Group theory and it's Applications to the Quantum Mechanics of atomic spectra " by Eugene P. Wigner

in chapter 4 The elements of quantum mechanics it is written

Consider a many dimensional space with as many coordinates as the system considered as position coordinates. Every arrangement of the positions of the particles of the system corresponds to a point in this multidimensional configuration space. This point will move in the course of time tracing out a curve by which the motion of the system can be completely described classically. There exists a fundamental correspondence between the classical motion of this point, the system point in configuration space, and the motion of a wave packet also considered in configuration space, if only we assume that the index of refraction for these waves is ##\sqrt{2m(E-V)}\over E##, where ##E## is the total energy of the system;##V## is the potential energy as a function in the configuration space.
What does the wave-packet and the refractive index implies here.How to interpret this?
 
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I do not know the index of refraction in this context. According to the formula you quote, it has physical dimension of ##L^{-1}T##, inverse of velocity, if he does not apply some convention of unit that you have not quoted there.
 

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