Finite Potential Well in Quantum Mechanics - Solutions and Energy States

Explore a 55-minute physics lecture that delves deep into the Finite Potential Well Problem in one dimension, examining quantum mechanics through the Schrodinger Equation. Master the derivation of wavefunction solutions, apply boundary conditions to obtain Transcendental equations, and learn graphical solving techniques. Understand how to determine the number of bound states in a finite well and calculate their corresponding energy levels. Through detailed mathematical analysis and step-by-step explanations, gain comprehensive insights into quantum tunneling, discrete energy states, and the behavior of particles within finite potential barriers. Progress from fundamental concepts through advanced calculations, including practical numerical methods for energy level determination.