Transcription of 4. Energy Levels - MIT OpenCourseWare
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4. Energy Levels Bound problems Energy in Square infinite well (particle in a box) Finite square well Quantum Mechanics in 3D: Angular momentum Schr odinger equation in spherical coordinates Angular momentum operator Spin angular momentum Addition of angular momentum Solutions to the Schr odinger equation in 3D The Hydrogen atom Atomic periodic structure The Harmonic Oscillator Potential Identical particles Bosons, fermions Exchange operator Pauli exclusion principle Bound problems In the previous chapter we studied stationary problems in which the system is best described as a (time-independent) wave, scattering and tunneling (that is, showing variation on its intensity) because of obstacles given by changes in the potential Energy .
The second condition thus does not set the value of A (that can be done by the normalization condition). In order to satisfy the condition, instead, we have to set . nπ. k. n L = nπ → k n = L for integer n. This condition then in turns sets the allowed values for the energies: 2 k 2 2 π 2 . n 2 . ≡ E. 1. n E. 2. n = = n
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