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CRC Press eBooks

Representation Theory

Nandita Rudra

Published Aug 19, 2019• 0 citations
Publisher

Abstract

In the first course of quantum mechanics one defines a wavefunction ψ α ( ξ, t ) to describe the state of the system. ψ α ( ξ . t ) is a function of the coordinates ξ at a particular instant of time t . The parameters α denote the quantum numbers of the physical quantities having well-defined values which describe the state ψ .
DOI
10.1201/9780429325762-2

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Quantum mechanics (QM) is the description of dynamics in the microscopic world of atoms, photons, electrons, etc. Similar to Newton’s law of dynamics, dp/dt = F, which is the statement on the time evolution of the dynamical physical state associated with matter, the Schrödinger equation iħdψ/dt = Hψ is the statement of the time evolution on the quantum physical state of matter, denoted with the function ψ ( x, t ). Though the wavefunction ψ ( x, t ) is not a dynamical quantity like momentum, the role of time in the description of dynamics is similar and straightforward, if the final results are interpreted as the average over a statistical ensemble (collection). In the conventional interpretation of quantum mechanics, the wavefunction is supposed to be the complete description of the physical state of the particle, like an electron or an atom. It is complex-valued, mathematically, and needs two real quantities for its specification. It evolves in ‘magnitude’ and ‘phase’ as the reference clock advances in time. The evolution progresses causally, connecting the past to the present and into the future, as one expects in dynamics. Thus, the variable called ‘time’ in the microscopic world of quantum mechanics is the same as the time that is familiar in our macroscopic world.