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Question 1: Barrier potential A particle of mass \( m \) is subjected to a finite square well potential: \[ V(x)=\left\{\begin{array}{cc} V_{0}, & 0a \). 1. Write the Schrödinger equation for \( x<0 \). Let \( k^{2}=\frac{2 m E}{\hbar^{2}} \). 2. Give the general solution of that equation. Call the constants \( A \) and \( B \). 3. Write the Schrödinger equation for \( x>a \) and solve it. Call the constants \( F \) and \( G \). 4. Write the Schrödinger equation for \( 0

1) For x<0, V=0 So, Schrodinger (Sch, henceforth) equation: ?h?22md2?dx2=E? ?d2?dx2+2mEh?2?=0 ?d2?dx2+k2?=0 where k=2mEh?2