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Published byAmanda Ferguson Modified over 9 years ago
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Lecture 2: A physical interpretation of QM Part I: Meaning of the wave function; the Born rule
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Schrödinger equation The Nobel Prize in Physics 1933 was awarded jointly to Erwin Schrödinger and Paul Adrien Maurice Dirac "for the discovery of new productive forms of atomic theory."
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Born interpretation The Nobel Prize in Physics 1954 was divided equally between Max Born "for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction"
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So, what is the wave-function?
It may be a wrong question to ask, as the wave-function is a mathematical construct (one among several others) that allows us to calculate what we are interested in (observables, i.e., something we can actually measure). Find the wave-function which satisfies a closed Eq and determines X Quantum observable, X, at t=0 Know: X, at a later time t=T Want to know: No closed equation for X… We certainly have seen such auxiliary concepts elsewhere in physics. For example: Neither scalar nor vector potential is directly observable, which does not surprise us, neither should we be surprised by the wave-function…
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Lecture 2: A physical interpretation of QM Part II: Operators
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Appearance of operators in Schrödinger’s “derivation”
Experimental fact: quantum electrons may exhibit wave-like properties Assume that they may be described by a plane-wave function: We have to reconcile it with Hence the free Schrodinger equation Generalize it to with We can write it as if we identify,
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Expectation values
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A physical interpretation of quantum theory Part III: Time-independent Schrödinger Eq. Eigenvalue problems
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Getting rid of the time derivative, when it’s not needed
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A simple (mathematical) example of an eigenvalue problem
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Operators, eigenvalues, and eigenvectors in QM: summary
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Lecture 2: A physical interpretation of QM Part IV: Superposition principle; Dirac notations; representations
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Superposition principle in quantum mechanics
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Simple reminder from linear algebra
x’ y’ x y
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How to choose a basis/representation
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