Question
Asked Dec 12, 2019
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The wavefunction of is Ψ(x) = Axe−αx2/2 for with energy E = 3αℏ2/2m
. Find the bounding potential V(x). Looking at the potential’s form, can you write down the two energy levels that are immediately above ??

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Step 1

Given:

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- a? -Cx (1) wavefunction, y=Axe Зай energy, E 2

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Step 2

Using wave equation

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-h d’w vx}w(x) = Ey(x)....(2) 2m dx

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Step 3

Derivate equation (1) w...

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-ax y= Axe -CxX -2ax -Ox dự Ae + Axe 2. de -cx? - cx? dự = Ae ? - ax Ae de again differentiate w.r.t x -ca - 2axAe d'y =-AXA. dx - Cox +a'x° Ae ? -ax +a²x³Ae -ax d'y = -3axAe ? dx %3D -a? d'y -(-за +а'x)х4е Ae dx d'w =(-3a +a²x²)w...(3) dr

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