Suppose a particle is described by a superposition of 1-D particle in the box wavefunctions as shown as below 4₁ = √√ ² sin ( x) n 0 = 1/64/₂ + 1/24/₂ + √2/24/3 √32 Use this setup to do the problems below 1. Show that Σ|c₂|² = 1 2. Explain, in plain language, why Σ|c₂ |² = 1 12 3. Calculate for ₁, V₂, Y using L=1Â (hint: only plug in the numerical value of L once you've calculated the integral). 4. Use your result from problem 3 to calculate for > and explain why the answer is sensible

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A: The normalized wave function for 2D potential well be given as, ψnx,ny=2Lx2LysinnxπxLxsinnyπyLy…

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Q: 1 = (x) %3D L/2

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A: The solution of this problem is following.

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Schrödinger equation

Schrödinger equation is a prominent equation in quantum mechanics. This equation is used to predict the behavior of quantum states or quantum particles. In quantum mechanics, the particles are treated as waves. A quantity called wave function is used to represent a quantum state. The wave function completely describes the quantum system. This equation can be used to study the particles like electrons, protons and, neutrons. It is also used to study the structure of hydrogen atoms and harmonic oscillators.