# Wave-packet in configuration space

• A
In summary, Wigner discusses the elements of quantum mechanics in his book "Group theory and its Applications to the Quantum Mechanics of atomic spectra." He explains that in a many-dimensional space with position coordinates, the motion of a system can be described by a point in configuration space. This point's movement corresponds to the classical motion of the system and the motion of a wave packet in configuration space, assuming a specific index of refraction. However, the meaning and interpretation of this refractive index is not clear.
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?

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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