What's that? Can you write down the Hamiltonian?sadegh4137 said:inverse harmonic oscillator
A propagator of inverse harmonic oscillator is a mathematical expression that describes the time evolution of a quantum mechanical system with a harmonic potential. It is used to calculate the probability of a particle moving from one position to another over a given period of time.
The propagator of inverse harmonic oscillator can be calculated using the Feynman path integral method, where all possible paths of a particle are considered and then summed over to find the overall probability. It can also be calculated using the Schrödinger equation.
The propagator of inverse harmonic oscillator is a fundamental tool in quantum mechanics as it allows for the calculation of the time evolution of a system. It is also used in various other areas of physics, such as statistical mechanics and quantum field theory.
The propagator of inverse harmonic oscillator has several key properties, including time reversal symmetry, translation invariance, and unitarity. It also satisfies the Schrödinger equation and the boundary conditions of the harmonic oscillator potential.
The propagator of inverse harmonic oscillator has many practical applications, such as predicting the behavior of quantum systems in various physical processes, such as chemical reactions and particle interactions. It is also used in the study of quantum computing and quantum information theory.