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snoopies622
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I stumbled over something reading Green's Matrix Mechanics (1965) this afternoon. There was an equation very similar to one I saw in Dirac's Lectures on Quantum Field Theory (1966), where he talks about the equivalence (or near equivalence) of the Schrödinger and Heisenberg formulations of ordinary quantum mechanics:
[tex]
U_{S} = e ^ {-iHt/ \hbar} U_{H} e^ {iHt/ \hbar }
[/tex]
I take it that the U's are matrices, but what are the exponential terms? Vectors? Other matrices? If H is a matrix, what does it mean to raise a real number (e) to the power of a matrix? If instead they are real numbers, wouldn't the two exponential terms then simply cancel each other out?
[tex]
U_{S} = e ^ {-iHt/ \hbar} U_{H} e^ {iHt/ \hbar }
[/tex]
I take it that the U's are matrices, but what are the exponential terms? Vectors? Other matrices? If H is a matrix, what does it mean to raise a real number (e) to the power of a matrix? If instead they are real numbers, wouldn't the two exponential terms then simply cancel each other out?