Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Chemical Sciences Basic Principles of Quantum Mechanics
The Wavefunction of 1D harmonic oscillator between x= +\(\infty \ \ and\ \ x= -\infty\) is given by \(ψ (x) = N (2x^2 -1)e^{-\frac{x^2}{2}} \). The value of N that Nornalizes the function ψ (x) is :
Given:\(\int_{-\infty}^{+\infty} x^{2n }e^{-x^2} dx = \frac{1.2.3.(2n-1)}{2^n} \sqrt{\pi}\)
1
\((\frac{1}{8\sqrt{\pi}})^{1/2}\)
2
\((\frac{1}{3\sqrt{\pi}})^{1/2}\)
3
\((\frac{1}{2\sqrt{\pi}})^{1/2}\)
4
\((\frac{1}{4\sqrt{\pi}})^{1/2}\)
5
Question Not Attempted