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Quantum Physics II, Lecture Notes 1 - MIT OpenCourseWare

WAVE MECHANICS B. Zwiebach September 13, 2013 Contents 1 The Schr odinger equation 1 2 Stationary Solutions 4 3 Properties of energy eigenstates in one dimension 10 4 The nature of the spectrum 12 5 Variational Principle 18 6 Position and momentum 22 1 The Schr odinger equation In classical mechanics the motion of a particle is usually described using the time-dependent position ix(t) as the dynamical variable. In wave mechanics the dynamical variable is a wave-function. This wavefunction depends on position and on time and it is a complex number it belongs to the complex numbers C (we denote the real numbers by R).

1 The Schrod¨ inger equation 1 . 2 Stationary Solutions 4 . 3 Properties of energy eigenstates in one dimension 10 . 4 The nature of the spectrum 12 . 5 Variational Principle 18 . 6 Position and momentum 22 . 1 The Schrodinger equation . In classical mechanics the motion of a particle is usually described using the time-dependent ...

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