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Published byEric Fausett Modified about 1 year ago

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Dirac’s Quantum Condition Classical mechanics relates two conjugated variables by using the Poisson bracket. Dirac’s quantum condition extends this relation to quantum mechanical operators: The commutator between two operators must relate to the classical Poisson bracket between the two corresponding functions through the following relationship Operators which follow Dirac’s quantum condition form an internally consistent set, though there may be more than one set (different representations) HW #2

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Poisson bracket and commutator For example, for f(x,p)= x and g(x,p)=p the Poisson bracket is

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Variance Finally, we can connect everything we know about commutators and the Dirac’s quantum condition and obtain the most fundamental property of the Quantum World individual measurements expectation value

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Uncertainty Principle For the product of the standard deviations of two properties of a quantum mechanical system whose state wavefunction is it can be shown (you’ll do it in your HW2)

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The Born Interpretation The explicit function representing a state of a system in a particular coordinate system and in a particular representation is called WAVEFUNCTION: Remember? Probability of an event is given by | | 2 where is a complex number (probability amplitude)

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cont Normalization: The probability of finding the particle SOMEWHERE in space and time MUST be =1 Wavefunctions which obey the eigenvalue equation are called eigenfunctions

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