IGNOU PHE 11 2018 - In a region of space a particle of mass m has a wavefunction:w

Question

In a region of space a particle of mass m has a wavefunction:

Image ignouacademy-com--p-particle-82895

where a is a positive constant. Calculate:
i) the normalization constant N
ii) the potential energy of the particle if the total energy of the particle is zero.

27 Jan 2018

Answer :

Word Count : 272

The given wavefunction of the particle is: \[ \psi(x) = N e^{-\frac{|x|}{a}} \] where \( N \) is the normalization constant and \( a \) is a positive constant. ### Step 1: Normalization Constant \( N \) To normalize the wavefunction, we require: \[ \int_{-\infty}^{\infty} |\psi(x)|^2 dx = 1 \] Substituting \( \psi(x) \): \[ \int_{-\infty}^{\infty} N^2 e^{-\frac{2|x|}{a}} dx = 1 \] Since the function is symmetric, we can write: \[ 2N^2 \int_0^{\infty} e^{-\frac{2x}{a}} dx = 1 \] Evaluating the integral: \[ \int_0^{\infty} e^{-\frac{2x}{a}} dx = \frac{a}{2} \] Thus, we

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