The Principles of Quantum Mechanics¶
Dirac, P. A. M. (1958). The Principles of Quantum Mechanics. Clarendon Press.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Conjugate Variables
- the canonical commutation relation [x̂, p̂] = iℏ quantum-mechanically
This sourceEstablishes canonical quantization q→q̂, p→p̂ and the canonical commutation relation [q̂,p̂]=iℏ as the fundamental quantum postulate; Dirac's 'q-numbers' and Poisson-bracket→commutator correspondence are the source for the relation cited. (archive.org copy is the 1958 4th edition of the same work.)
- the canonical commutation relation [x̂, p̂] = iℏ quantum-mechanically
Domain-specific¶
- Hamiltonian Mechanics
- Analytical / classical mechanics — the canonical formulation beyond a few degrees of freedom: celestial mechanics, rigid bodies, and constrained systems. Statistical mechanics — the Liouville equation for ensemble flow on phase space, with Hamiltonian flow preserving the Liouville measure as the microscopic foundation of equilibrium theory. Quantum mechanics — canonical quantization promoting \(H\) to a self-adjoint \(\hat H\) and the Poisson bracket to \([\hat q,\hat p]=i\hbar\), generating unitary evolution under Schrödinger's equation
SupportedVerified against the work's full text
“in terms of which Schrdinger gave his original formulation of quantum mechanics”
- Analytical / classical mechanics — the canonical formulation beyond a few degrees of freedom: celestial mechanics, rigid bodies, and constrained systems. Statistical mechanics — the Liouville equation for ensemble flow on phase space, with Hamiltonian flow preserving the Liouville measure as the microscopic foundation of equilibrium theory. Quantum mechanics — canonical quantization promoting \(H\) to a self-adjoint \(\hat H\) and the Poisson bracket to \([\hat q,\hat p]=i\hbar\), generating unitary evolution under Schrödinger's equation
Verification¶
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