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Quantum Mechanics Mock Tests

28 questions available

Quantum Mechanics Mock Test 1

Questions: 28

Sample Questions

GATE Physics
The de Broglie wavelength of a particle with momentum p is:
A h/p
B h·p
C p/h
D ℏ/p
GATE Physics
The Dirac equation for a free relativistic particle of mass m is:
A (iℏγᵘ∂ᵤ - mc)ψ = 0
B (iℏ∂/∂t - mc²)ψ = 0
C (-ℏ²∇²/(2m) - E)ψ = 0
D (iℏ∂ψ/∂t = (p²/2m)ψ
GATE Physics
The energy levels of the hydrogen atom (ignoring fine structure) are given by:
A E_n = -13.6 eV/n²
B E_n = -13.6 eV/n
C E_n = -13.6 eV·n²
D E_n = -13.6 eV/(n+1)
GATE Physics
The Hamiltonian of a simple harmonic oscillator H = p²/(2m) + (1/2)mω²x² can be written in terms of creation (a†) and annihilation (a) operators as:
A H = ℏω(a†a + 1/2)
B H = ℏω(a†a)
C H = ℏω(a + a†)
D H = ℏω(a² + a†²)
GATE Physics
A particle of mass m is confined in a one-dimensional infinite potential well of width L (0 < x < L). The energy of the nth excited state is:
A n²h²/(8mL²)
B n²h²/(2mL²)
C nπℏ²/(2mL²)
D n²ℏ²/(2mL²)
GATE Physics
The condition for a function to be Hermitian is that its operator satisfies:
A ⟨φ|Aψ⟩ = ⟨Aφ|ψ⟩ for all φ, ψ in the Hilbert space
B ⟨φ|Aψ⟩ = -⟨Aφ|ψ⟩ for all φ, ψ
C ⟨φ|Aψ⟩ = 0 for all φ, ψ
D ⟨φ|Aψ⟩ = ⟨φ|ψ⟩ for all φ, ψ
GATE Physics
The angular momentum operator L_z in quantum mechanics, in spherical coordinates, is:
A -iℏ ∂/∂φ
B iℏ ∂/∂φ
C -iℏ ∂/∂θ
D -iℏ(r sin θ) ∂/∂φ
GATE Physics
In time-independent perturbation theory, the first-order correction to the energy eigenvalue E_n^(1) is:
A ⟨ψ_n^(0)|H'|ψ_n^(0)⟩
B Σ_{m≠n} |⟨ψ_m^(0)|H'|ψ_n^(0)⟩|²/(E_n^(0) - E_m^(0))
C ⟨ψ_n^(0)|H'²|ψ_n^(0)⟩
D ⟨ψ_n^(0)|H'|ψ_m^(0)⟩

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