IIT JAM & CSIR NET - Chemical Sciences

Quantum Chemistry & Molecular Spectroscopy question bank (Physical Chemistry, Quantum & Thermodynamics)

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Q1.

[Physical Chemistry, Quantum & Thermodynamics Problem #1] Regarding Hamiltonian formulation of classical mechanics: Which of the following analytical formulations is correct?

(A)

H = T - V representing the total potential Lagrangian

(B)

d/dt(∂L/∂q_dot) - ∂L/∂q = 0

(C)

dq_i/dt = -∂H/∂p_i and dp_i/dt = ∂H/∂q_i

(D)

Hamilton's canonical equations are dq_i/dt = ∂H/∂p_i and dp_i/dt = -∂H/∂q_i

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Q2.

[Physical Chemistry, Quantum & Thermodynamics Problem #2] Regarding energy eigenvalues of a particle of mass m in a 1D infinite potential well of width L: Which of the following analytical formulations is correct?

(A)

E_n = ħ^2 k^2 / (4 m L)

(B)

E_n = (n^2 ħ^2) / (8 m L^2)

(C)

E_n = (n^2 π^2 ħ^2) / (2 m L^2), where n = 1, 2, 3...

(D)

E_n = (n + 1/2) ħ ω

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