1976/10/01 by Leon Cohen · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Quantum Mechanics and Applications #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Mathematics #Phase space #Quantization (signal processing) #Eigenfunction #Variational principle #Mathematical formulation of quantum mechanics #Hamiltonian (control theory) #Eigenvalues and eigenvectors #Quantum statistical mechanics #Quantum mechanics #Mathematical analysis #Classical mechanics #Quantum #Physics #Supersymmetric quantum mechanics
paper · doi:10.1063/1.522807
openalex publication_date 1976/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
The problem of quantization in the phase-space formulation of quantum mechanics is considered. An integral equation for the phase-space eigenfunctions is derived which is equivalent to the standard eigenvalue equation for a quantum mechanical operator. A differential form is also given. A variational principle is derived for quasiprobability distributions. It is shown that the expected value of the classical Hamiltonian calculated with a trial quasiprobability distribution will be greater than the ground state energy only if the distribution is chosen from a certain class of functions. The notion of ψ-representability is introduced to classify these functions. They represent distributions which correspond to possible quantum mechanical states. Also, a general relation is given between different distribution functions.