Quantum mechanics without an equation of motion

Journal Article · Wed Jun 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3602278· OSTI ID:21501349

Alhaidari, A D ^[1]

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1. Saudi Center for Theoretical Physics, Jeddah 21438 (Saudi Arabia)

We propose a formulation of quantum mechanics for a finite level system whose potential function is not realizable and/or analytic solution of the wave equation is not feasible. The system's wavefunction is written as an infinite sum in a complete set of square integrable functions. Interaction in the theory is introduced in function space by a real finite tridiagonal symmetric matrix. The expansion coefficients of the wavefunction satisfy a three-term recursion relation incorporating the parameters of the interaction. Information about the structure and dynamics of the system is contained in the scattering matrix, which is defined in the usual way. The bound state energy spectrum (system's structure) is finite. Apart from the 2M- 1 dimensionless parameters of the interaction matrix, whose rank is M, the theory has one additional scale parameter. In the development, we utilize the kinematic tools of the J-matrix method.

• OSTI ID: 21501349
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 6; Other Information: DOI: 10.1063/1.3602278; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
ANALYTICAL SOLUTION
BOUND STATE
ENERGY SPECTRA
EQUATIONS OF MOTION
INTEGRAL CALCULUS
INTEGRAL EQUATIONS
MATHEMATICAL SPACE
MATRICES
QUANTUM MECHANICS
SYMMETRY
WAVE EQUATIONS
WAVE FUNCTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
SPECTRA