Applications of hyperdifferential operators to quantum mechanics

DOI10.1007/BF01907033zbMath0223.35008OpenAlexW2044422219MaRDI QIDQ2548022

Marvin Miller, Stanly L. Steinberg

Publication date: 1971

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01907033

Mathematics Subject Classification ID

Transform methods (e.g., integral transforms) applied to PDEs (35A22) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

Related Items (5)

Calculus of variations with hyperdifferential operators from Tabasaki-Takebe-Toda lattice arguments ⋮ An application of hyperdifferential operators to holomorphic quantization ⋮ Canonical transforms. I. Complex linear transforms ⋮ Canonical transforms. II. Complex radial transforms ⋮ Applications of the Lie algebraic formulas of Baker, Campbell, Hausdorff and Zassenhaus to the calculation of explicit solutions of partial differential equations

Cites Work

• Pseudo-Fokker Planck equations and hyperdifferential operators
• Phase-Space Formulation of the Dynamics of Canonical Variables
• Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0
• Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by ∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x, y, t = 0) = Φ(x, y)
• An algebra of pseudo‐differential operators
• Exponential Operators and Parameter Differentiation in Quantum Physics
• Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x,y,0)=Φ(x,y)
• Closed-Form Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 by Normal-Ordering Exponential Operators
• On the Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0

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