# Quantum Mechanics: Physical Problems in one-dimension

Other, , Prof. Donylee

Updated On 02 Feb, 19

Other, , Prof. Donylee

Updated On 02 Feb, 19

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

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4.1 ( 11 )

The Potential Barrier, case E ≥ V₀

Now, with an algebraic expression for the transmission coefficient, we adjust energy values and observe what happens to the particle.

1. With E ≫ V₀ - particles dont feel effect of barrier.

2. For certain energy values, all the particles will get transmitted over. These values, called energy eigenvalues, coincides with that of the infinite square well potential showcasing the phenomena of resonance.

Notice that there are more than one way to achieve full transmission.

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

Sam

Sep 12, 2018

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

Dembe

March 29, 2019

Great course. Thank you very much.