Does this expression has an exact solution?

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Discussion Overview

The discussion revolves around the question of whether a specific Hamiltonian expression has an exact solution. Participants explore methods for solving the Hamiltonian, particularly through coordinate transformations to simplify the potential term.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant asks how to solve a Hamiltonian and whether it has an exact solution.
  • Another participant asserts that there is an exact solution and suggests making a coordinate transformation to diagonalize the potential term.
  • A follow-up question is posed regarding the effect of changing a parameter (C to Cij) on the existence of an exact solution, to which a participant responds affirmatively.
  • A link to a resource on quadratic forms is provided for further reference.

Areas of Agreement / Disagreement

Participants generally agree that the Hamiltonian has an exact solution, but the implications of changing parameters remain less clear, as the discussion does not resolve whether this change affects the solution.

Contextual Notes

The discussion does not clarify specific assumptions regarding the Hamiltonian or the nature of the potential term, nor does it address the mathematical steps involved in the proposed transformations.

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how to solve this hamilition? and Does this expression has an exact solution?
 

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It has an exact solution. Try to make a coordinate transformation so that the potential term is diagonal in the new coordinates.
 
weejee said:
It has an exact solution. Try to make a coordinate transformation so that the potential term is diagonal in the new coordinates.

if I change the C to Cij , it still has an exact solution ?
 

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