Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 4.2, Problem 4.12P
To determine

The radial wave function of R30,R31andR32

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Show that a gaussian psi (x) = e ^(-ax^2) can be an eigenfunction of H(hat) for harmonic oscillator 1. Compute T(hat)*psi 2. Compute Vhat* psi - assume V operator is 1/2w^2x^2 3. Write out Hbar*psi and identify terms so Hber*psi=E*psi is true 4. From cancellation find a 5. insert back a to Schrodinger eq above and find E
Suppose that you have the Lagrangian L = 21 (;² + è°r2) + 420 for a 2D 20 system in plane polar coordinates (r, 0). Determine the pr and pe canonical coordinates.
The Hamiltonian of a one-dimensional harmonic oscillator can be written in natural units (m = hbar= ω = 1) as: (image1) Where ˆa =(ˆx+ipˆ)/√2, and ˆa† =(ˆx−ipˆ)/√2   One of the proper functions is: (image2)     Find the two eigenfunctions closest in energy to the function ψa (you don't have to normalize) .
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