Griffiths QM Problem 4.46 | 3D Harmonic Oscillator: Energy & Degeneracy скачать в хорошем качестве

Griffiths QM Problem 4.46 | 3D Harmonic Oscillator: Energy & Degeneracy

In this video, we solve Problem 4.46 from a Quantum Mechanics textbook step by step. We analyze the three-dimensional harmonic oscillator, where the potential is given by: V(r) = (1/2) m ω² r² ✅ (a) Show that separation of variables in Cartesian coordinates transforms the problem into three one-dimensional harmonic oscillators, and determine the allowed energy levels: Eₙ = (n + 3/2) ħω ✅ (b) Determine the degeneracy d(n) of the energy level Eₙ, and understand how multiple quantum states can share the same total energy. 💡 You will learn how to: Separate variables in the Schrödinger equation for 3D systems Use 1D oscillator results to find 3D energy levels Understand degeneracy in multi-dimensional quantum systems Interpret quantum numbers (nₓ, n_y, n_z) and their combinations Perfect for students studying Quantum Mechanics, Harmonic Oscillators, and Energy Quantization! 🔔 Subscribe for more step-by-step physics problem explanations — covering quantum mechanics, angular momentum, and energy eigenstates!