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Results tagged with commutator
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user 197570
A mathematical construct quantifying the difference in effect of applying two operators in two alternate successions. It is the defining product of a Lie algebra, the efficient underlying description of Lie groups, of use in several areas of physics, most notably quantum field theory.
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Exponentiated Commutation Relations
A proof about the exponentiated commutation relations is mentioned In this book page 285:
The exponentiated momentum operators satisfy:
$(e^{itP_j}\psi)(\textbf{x})=\psi(\textbf{x}+t\hbar \textbf{e}_ …
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What does the comma mean in this commutation rule between quantum operators?
The Theorem about quantum operators commutation relation says:
Consider pairs $(U, V )$ of unitary representations on a
Hilbert space $H$, satisfying the commutation rule:
$$U(x) V(y)=\exp (i …
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Addition of a constant to the operator due to quantization
Groenewold in his book On the Principles of Elementary Quantum Mechanics (1946, Springer Netherlands) page 45, maps the canonical momentum $p^2$ in the classical phase space to a general canonical ope …
- 279
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Is Planck's Constant Really a Constant?
I am going through Groenewold's theorem and in his book: On The Principles of Elementary Quantum Mechanics, page 8, eq. 1.30:
$$[\mathbf{p}, \mathbf{q}]=1\left(\text { i.e. } \mathbf{p
q}-\mathbf …
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