Renormalization Group Transformation for the Wave Function

TL;DR

This paper explores how the Hamiltonian of a nonrelativistic particle depends on measurement resolution, using a renormalization group approach to understand the transformation of the wave function and observables.

Contribution

It introduces a renormalization group transformation for the wave function that accounts for finite measurement resolution effects on the Hamiltonian.

Findings

Hamiltonian depends on measurement resolution

Renormalization group transformation models this dependence

Quadratic Hamiltonian systems are analyzed in detail

Abstract

The problem considered here is the determination of the hamiltonian of a first quantized nonrelativistic particle by the help of some measurements of the location with a finite resolution. The resulting hamiltonian depends on the resolution of the measuring device. This dependence is reproduced by the help of a blocking transformation on the wave function. The systems with quadratic hamiltonian are studied in details. The representation of the renormalization group in the space of observables is identified.