1. Infinite-Potential Well RevisitedV(x)V = 0V = 0V = 0Lx =2x = +52Consider the quantum mechanics of a particle with mass m that is confined in the infinitpotential well of width L as shown above.(a) By direct substitution into the time-independent Schrödinger,h? d²µ(x)+V(x)µ(x) = EÞ(x)2m dx?show that the wavefunction of the particle isPn(x) = Asin+with the quantized energy levels given byh?n²n?E = En =2ml?where n = 1,2,3, ... (b) Does the wavefunction , (x) satisfy the appropriate boundary conditions?(c) What is the value of the normalization constant A?(d) Using the trigonometric identitysin(a + B) = sin(æ)cos(ß) + cos(a)sin(ß)show that w, (x) can be classified into wavefunctions with odd and even symmetries i.e.,sinп оddUn(x) = A{cosп еven

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1. Infinite-Potential Well Revisited V(x) V = 0 V = ∞ V = 0 L x = +5 x = 2 Consider the quantum mechanics of a particle with mass m that is confined in the infin