x # Quantum Mechanics: Physical Problems in one-dimension

Other, , Prof. Donylee

Updated On 02 Feb, 19

##### Overview

Contents:
Physical Problems in one-dimension - Continuous States - Analyzing the Solutions - Are continuous states physical - A Gaussian Wave Packet - Calculating our wave packet - Solving the Schrdinger Equ-Description of Plane Waves - Probability Current Density - Calculating R and T- Explaining Quantum Behavior - Particle-like gets stopped - The strange evanescent wave - Deriving discrete energy value - What is zero-point energy? - Unusual probability densities - The scattering problem

Ratio transmitted particles - Energy values and Resonance - Full transmission of part.- Setting the situation - Deciphering the wave-like particle - Penetrating the potential barrier - Further analysis of T - The WKB approximation method - Introduction - Unphysical Solutions - Fourier transform revisit - Outside the well - Anti/symmetric solutions - Boundary conditions- A graphical solution- Discrete energy specturm

## Lecture 29: QM6.5 Finite Square Well E ≤ V₀ - Antisymmetric solutions

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###### Lecture Details

The Finite Square Well Potential, case E ≤ V₀
Solving the Schrödinger equation inside the well is a little different. Recall the theorem that bound states of a particle in a symmetric potential have definite parity they are either even or odd functions.

V(-x) = V(x) ⇒ Ψ(-x) = ±Ψ(x)

We use this theorem to progress in the problem.

For an in-depth study, check out www.gaussianmath.com

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Excellent course helped me understand topic that i couldn't while attendinfg my college. 