Lecture_13 - PHYS PHYS342 Fall2011 Lecture 13 Schrdingers...

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PHYS 342 Fall 2011 Lecture 13: Schrödinger’s Equation in 2 dimensions Schrödinger s Equation in 2 dimensions Ron Reifenberger Birck Nanotechnology Center Purdue University Lecture 13 1
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F d mi l s st m th xists f ti Ψ th t is If we know the wavefunction, we know everything it is possible to know For every dynamical system, there exists a wavefunction that is a continuous, square-integrable*, single-valued function of the coordinates of all the particles and of time. If you know Ψ , all possible predictions about the physical properties of the system can be obtained. “The coordinates of all the particles”? x F i l ti l i di i For a single particle moving in one dimension: , x t For a single particle in one dimension: For a single particle moving in three dimensions: , t r For a single particle in a superposition of two quantum states, a and b: , ( , ) ( , ) a b x t A x t B x t For two particles moving in three dimensions: 1 2 , , t r r   * Square-integrable means that the normalization integral is finite 2
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