3 Dimensional Harmonic Oscillator | Lecture Note - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

428

Pages:

3
Author:

Jabin F.

3-D Harmonic Oscillator:- 1. Anisotropic Harmonic Oscillator 2. Iso tropic Harmonic Oscillator 1. Anisotropic H.O.:- V(x,y,z) = 1/2 m(w_x^2)(x²) + 1/2 m(w_x^2)y² + 1/2 m(w_z^2)z² 2 2 2 if wx ≠ Wy ≠ Wz or wx = Wy ≠ Wz Wy ≠ Wz V(x) + V(y) + V(z) 2. Isotropic H.O:) if Wn= Wy = Wz = W V(x,y,z) = 1/2mw² (x²+y²+z²) = 1/2 mw²y² = 1/2 mw^2x² + 1/2 mw^2y² + 1/2 mw^2z² = V(x) + V(y) + V(2) Text: Mathematical symbols, equations, and potentially Korean characters. Numbers: Numerical values and coefficients within the equations. Layout: The content is arranged in a somewhat disorganized manner with multiple lines of equations and text. Specifics: There are multiple instances of the number 22 and the symbol "e". The concept of isotropic harmonic oscillator is mentioned. Mathematical expressions involving variables like x, y, z, m, and w are present. There might be Korean characters or words included. Potential Issues: The handwriting is not entirely clear, making some symbols and characters difficult to interpret. The lack of clear structure and context makes it challenging to fully understand the content. The presence of Korean text might require additional language expertise for accurate interpretation. Nx + ny + nz = n, nx, ny, nz = 0, 1, 2, 3, ...∞ The ground state energy⇒ E₀₀₀ = 3/2ħω₀₀₀ =Ψ₀₀₀ The energy of first excited state⇒ E = 5/2 ħω Here n = 1, Nx + Ny + Nz = 1 => (Nx, Ny, Nz) = (1, 0, 0), (0, 1, 0), (0, 0, 1) Here wave fn: Ψ₁₀₀, Ψ₀₁₀, Ψ₀₀₁ ∴ E=> is 3-fold degenerate

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