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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). When all three dimensions of space are relevant we write the wavefunction as (ix, t) C . ( ) When only one spatial dimension is relevant we write it as (x, t) C.

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). When all three dimensions of space are relevant we write the wavefunction as ...

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