Harmonic Oscillator - Physical Chemistry - Chemistry Previous Year Questions

1

2011 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2011

The wave function for a Harmonic oscillator described by Nx exp(-cx²/2) has

A

one maximum only

B

one maximum, one minimum only

C

two maxima, one minimum only

D

two maxima, two minima only

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2

2012 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2012

The wavefunction of a 1-D harmonic oscillator between \(x=+\infty\) and \(x=-\infty\) is given by \(\psi(x) = N(2x^2 - 1)e^{-x^2/2}\). The value of \(N\) that normalizes the function \(\psi(x)\) is
(Given: \(\int_{-\infty}^{\infty} x^{2n} e^{-x^2} dx = \frac{1 \cdot 3 \cdot 5 \cdots (2n-1)}{2^n} \sqrt{\pi}\))

A

\(\left(\frac{1}{8\sqrt{\pi}}\right)^{1/2}\)

B

\(\left(\frac{1}{3\sqrt{\pi}}\right)^{1/2}\)

C

\(\left(\frac{1}{2\sqrt{\pi}}\right)^{1/2}\)

D

\(\left(\frac{1}{4\sqrt{\pi}}\right)^{1/2}\)

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3

2013 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2013

\( e^{-2x^2} \) is an eigen function of the operator \( \left( \frac{d^2}{dx^2} - 16x^2 \right) \). The corresponding eigen value is

A

+4

B

-4

C

+2

D

-2

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4

2013 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2013

The infrared spectrum of HCl gas shows an absorption band centered at 2885 cm^-1. The zero point energy of HCl molecule under harmonic oscillator approximation is

A

\(2.8665 \times 10^{-22} \) J

B

\(2.8665 \times 10^{-20} \) J

C

\(5.7330 \times 10^{-22} \) J

D

\(5.7330 \times 10^{-20} \) J

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5

2019 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2019

Consider a two dimensional harmonic oscillator with angular frequency ω_x = 2ω_y = 6.5 × 10¹⁴ rad s⁻¹. The wavelength of x polarized light required for the excitation of a particle from its ground state to the next allowed excited state is ______ × 10⁻⁶ m. (Round off to one decimal place)
(Speed of light c = 3.0 × 10⁸ m s⁻¹)

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6

2025 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2025

The ratio of the fundamental vibrational frequencies (ν₁₃C₁₆O / ν₁₂C₁₆O) of two diatomic molecules ¹³C¹⁶O and ¹²C¹⁶O, considering their force constants to be the same, is______ (rounded off to two decimal places).

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7

2007 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2007

The quantum state of a particle moving in a circular path in a plane is given by
Ψ_m(φ) = (1/√(2π))e^imφ, m = 0, ±1, ±2, ...
When a perturbation H₁ = P cos φ is applied (P is a constant), what will be the first order correction to the energy of the m^th state

A

0

B

P/(2π)

C

P/(4π)

D

Pm²/(4π²)

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8

2017 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2017

The lowest energy of a quantum mechanical one-dimensional simple harmonic oscillator is 300 cm^-1. The energy (in cm^-1) of the next higher level is ______________

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9

2018 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2018

A one-dimensional anharmonic oscillator is treated by perturbation theory. The harmonic oscillator is used as the unperturbed system and the perturbation is \(\frac{1}{6}\gamma x^3\) (γ is a constant).
Using only the first order correction, the total ground state energy of the anharmonic oscillator is
(Note: For a one-dimensional harmonic oscillator \(\psi_0(x) = (\frac{\alpha}{\pi})^{1/4} e^{-\alpha x^2/2}\); \(\alpha = (\frac{k\mu}{\hbar^2})^{1/2}\))

A

\(\frac{1}{2}\hbar (\frac{k}{\mu})^{1/2}\)

B

\((\frac{1}{2}+\frac{\gamma}{6})\hbar (\frac{k}{\mu})^{1/2}\)

C

\((\frac{1}{2}+\frac{\gamma}{3})\hbar (\frac{k}{\mu})^{1/2}\)

D

\((\frac{1}{2}+\frac{\gamma}{12})\hbar (\frac{k}{\mu})^{1/2}\)

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10

2026 · Chemistry · Physical Chemistry · Harmonic Oscillator

Chemistry (CY) 2026

The correct option for the average value of kinetic energy and the average value of potential energy of a one-dimensional harmonic oscillator with frequency ν in its ground state is

A

\(\frac{h\nu}{2}\) and \(\frac{h\nu}{4}\), respectively

B

\(\frac{h\nu}{2}\) and \(\frac{h\nu}{2}\), respectively

C

\(\frac{h\nu}{4}\) and \(\frac{h\nu}{4}\), respectively

D

\(\frac{h\nu}{4}\) and \(\frac{h\nu}{2}\), respectively

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