Finite dimensional quantum mechanics
Thesis/Dissertation
·
OSTI ID:6205427
The basic properties of nonrelativistic finite-dimensional quantum mechanics are presented. Position, momentum and Hamiltonian operators are introduced. The space of states in the case is the space C/sup r/. Properties of position and momentum operators are studied. Dynamics of the particles is considered. An Approximation Theorem is proved: finite dimentional quantum mechanics approximates ordinary quantum mechanics and the approximation gets better as the dimension increases. Second quantization, the symmetric and antisymmetric Fock spaces are discussed. It is shown that the Hilbert space L/sup 2/(R/sub 3/) of a single nonrelativistic particle p is the second quantization of the finite-dimensional space C/sup 3/. Creation, annihilation and field operators are introduced and represented in terms of different operators. A Theorem is proved which states that there is no conventional scattering in finite dimensional quantum mechanics. An isomorphism between SV and L/sup 2/(R/sup r/) is shown to be the decomposition by generalized eigenfunctions of field operators. Corresponding spaces of these and generalized functions are constructed. A functional space isomorphism is obtained for the complete tensor product of a finite dimensional space V = C/sup r/. Irreducible representations of the symmetry group in a complete tensor are constructed. Physical applications to elementary particles and quarks are briefly discussed.
- Research Organization:
- Denver Univ., CO (USA)
- OSTI ID:
- 6205427
- Country of Publication:
- United States
- Language:
- English
Similar Records
Field operators and their spectral properties in finite-dimensional quantum field theory
Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods
Twisted scalar and spinor strings in Minkowski spacetime
Journal Article
·
Thu Feb 28 23:00:00 EST 1985
· Found. Phys.; (United States)
·
OSTI ID:5547153
Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods
Journal Article
·
Fri Nov 14 23:00:00 EST 2014
· Annals of Physics (New York)
·
OSTI ID:22403432
Twisted scalar and spinor strings in Minkowski spacetime
Journal Article
·
Thu Feb 14 23:00:00 EST 1980
· Phys. Rev., D; (United States)
·
OSTI ID:5660439