Objective:

To demonstrate and explain the behavior of quantum particles in infinite and finite potential wells using graphical representations, and to explore various scenarios and solutions within quantum mechanics.

SOME FACTS:

(1) The time-independent Schrödinger equation, is fundamental in quantum mechanics. Understanding how to solve this equation for different potential functions V(x) is essential for analyzing the behavior of particles in potential wells.

(2) In both infinite and finite potential wells, particles occupy discrete energy levels. In an infinite well, these levels are given by 𝐸𝑛= ​ . In a finite well, solving the Schrödinger equation with boundary conditions reveals a set of quantized energy levels, which are typically lower than those in an infinite well due to the possibility of tunneling.

Step-1: (a) Click on Bring button to display the structures . Step-1: (a) Click over the structure to choose for analysis .

In an infinite potential well, the potential V(x) is zero inside the well and infinite outside, confining the particle strictly within a width L. And the probability of finding electrons at infinite potential is 0. Start Analysis

Case -1 Visualization of ψ(x) in an Infinite Potential Well

Input the value of n

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Case - 2 Visualization of ψ(x) in a finite Potential Well

Input the value of n, Potential and length

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