Suppose there are n particles in 3 dimension space coupled to one another via harmonic oscillator potential. Is it possible to solve it quantum mechanically exactly in closed form ? Kindly someone suggest reference as well to understand this better.
Sure. The action is quadratic in the dynamical variables, so all correlation functions can be expressed as products of the 2-point function, the propagator.
Alternatively, the energy can be diagonalized by a Fourier transform and the system in the new coordinates, becomes that of n decoupled oscillators.
Both are described in any textbook on quantum field theory these days.
To give a simpler answer, an ordered distribution of atoms connected by springs
is a standard problem giving rise to phonons in the harmonic approximation, answer found in books of Solid State Physics.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Quantum Physics
- Quantum Mechanics