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L9-10 - Richard Feynman I think it is safe to say that no...

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…I think it is safe to say that no one understands Quantum Mechanics… Richard Feynman
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Postulate 1: The state of a quantum mechanical system is completely specified by a function Ψ ( r ,t) that depends on the coordinates of the particle(s) and on time. This function, called the wave function or state function, has the important property that Ψ ( r ,t) Ψ ( r ,t) is the probability that the particle lies in the volume element d τ located at r at time t . The wavefunction is normalized and “well behaved” (single valued, continuous with continuous derivative) Acceptable as wavefunctions? exp (-x) between 0 and infinity exp (-x) between –infinity and +infinity 1/sin(x) in (-1,1) exp (-|x|) between –infinity and +infinity
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Postulate 2: To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics. Real eigenvalues and orthogonal eigenfunctions
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Angular momentum Total energy Multiply by Potential energy Kinetic energy Momentum Multiply by Position Operation Symbol Symbol Name Operator Operator Observable Observable
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Angular momentum Classical definition: Quantum Mechanical definition: Cross product
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The eigenfunctions of quantum
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