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a) The time-dependent Schrödinger equation is given by the expression, iℏ∂t∂ψ(r,t)=[−2mℏ2∇2+V(r)]ψ(r,t) i. Define all
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a) The time-dependent Schrödinger equation is given by the expression, iℏ∂t∂ψ(r,t)=[−2mℏ2∇2+V(r)]ψ(r,t) i. Define all
a) The time-dependent Schrödinger equation is given by the expression, iℏ∂t∂ψ(r,t)=[−2mℏ2∇2+V(r)]ψ(r,t) i. Define all the symbols used. [2] ii. By using the method of separation variables, show that the solution of the Schrödinger equation is: ψ(r,t)=Bφ(r)e−Σ˙Et/ℏ [5] iii. State any three properties of the wave function in a(ii) above with well-defined value E of the total energy, defining any (new) symbols used respectively in each case. [3] b) A particle of mass, m, is moving freely in a plane bounded in the intervals 0≤x≤a and 0≤y≤b. Using the time-independent Schrödinger equation and the method of separation of variables, find the; i. eigen functions of that particle. ii. normalized eigen function. [5] iii. corresponding energy eigenvalues. [2]
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