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Harmonic oscillator – series solution
Required math: calculus Required physics: harmonic oscillator Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Sec 2.3. The complete...
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Hermite polynomials
Required math: calculus Required physics: none Hermite polynomials turn up in the solution of the Schrödinger equation for the harmonic oscillator. Most quantum mechanics textbooks quote the properties...
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Harmonic oscillator – Hermite polynomials
Required math: calculus Required physics: harmonic oscillator Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Sec 2.3. When we solve the...
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Harmonic oscillator – example starting state
Required math: calculus Required physics: Schrödinger equation References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.41. Suppose a...
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Half-harmonic oscillator
Required math: calculus Required physics: Schrödinger equation References: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Problem 2.42. Suppose we...
View ArticleHarmonic oscillator: Hermite polynomials and orthogonality of eigenfunctions
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 7.3, Exercises 7.3.2 – 7.3.3. The eigenfunctions of the harmonic oscillator are given by where is a Hermite polynomial. The...
View ArticleHarmonic oscillator: matrix elements using Hermite polynomials
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 7.3, Exercise 7.3.4. Earlier, we found the matrix elements of and of the harmonic oscillator using the raising and lowering...
View ArticleHarmonic oscillator: momentum space functions and Hermite polynomial...
Shankar, R. (1994), Principles of Quantum Mechanics, Plenum Press. Section 7.5, Exercises 7.5.1 – 7.5.3. Earlier, we found the position space energy eigenfunctions of the harmonic oscillator to be...
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