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In: Physics

A particle of mass m is confined to a finite potential energy well of width L....

A particle of mass m is confined to a finite potential energy well of width L. The equations describing the potential are

U=U₀ x<0

U=0 0 < x < L

U=U₀ x > L

Take a solution to the time-independent Schrodinger equation of energy E (E < U₀) to have the form

A exp(-k₁ x) + B exp(k₁ x) x < 0

C cos(-k₂ x) + D sin(k₂ x) 0 < x < L

F exp(-k₃ x) + G exp(k₃ x) x > L

Which of the following statements is not correct for this solution?

C cos(-k₂ L) + D sin(k₂ L) = F exp(-k₃ L)

The wave function is continuous at x=0 and x=L

k_1=sqrt(2m( U₀-E ))/hbar

k₁=k₃

B=0

The first derivative of the wave function is continuous at x=0 and x=L

Expert Solution

genius_generous answered 8 months ago

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