The energy levels of a particle of mass m in a potential of the form are given, in terms of quantum number n = 0, 1, 2, 3, . . ., by
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Quantum Mechanics
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The quantum mechanical operator for the momentum of a particle moving in one dimension is given by
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and represent two physical characteristics of a quantum system. If is Hermitian, then for the product to be Hermitian, it is sufficient that
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A particle of mass m is confined in an infinite potential well V\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{0,}&{{\text{if }}0 < x < L} \\
{\infty ,}&{{\text{otherwise}}}
\end{array}} \right.
It is subjected to a perturbing potential within the well. Let E(1) and E(2) be the corrections to the ground state energy in the first and second order in V0.
Which of the following is correct?
It is subjected to a perturbing potential within the well. Let E(1) and E(2) be the corrections to the ground state energy in the first and second order in V0.
Which of the following is correct?
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A particle is incident with a constant energy E on a one-dimensional potential barrier as shown in the figure.
The wave functions in regions I and II are respectively
The wave functions in regions I and II are respectively
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Which one of the functions given below represents the bound state eigen function of the operator in the region, 0 ≤ x < , with the eigen value -4?
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The degeneracy of the n = 2 level for a three-dimensional isotropic oscillator is
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A parallel beam of infrared radiation of wavelength of 1.01 × 10-6 m is incident normally on a screen with two slits 5 × 10-6 m apart and the resulting interference pattern is observed on a distant screen. What is the largest number of maxima that can be observed on the screen?
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A quantum particle of mass m is confined to a square region in XOY-plane whose vertices are given by (0, 0), (L, 0), (L, L) and (0, L). Which of the following represents an admissible wave function of the particle (for I, m, n positive integers)?
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A particle has the wave function (x, t) = A[exp (iωt) cos (kx)]. Which one of the following is correct?
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If is the total cross-section and f(θ), θ being the angle of scattering, is the scattering amplitude for a quantum mechanical elastic scattering by a spherically symmetric potential, then which of the following is true? Note that k is the magnitude of the wave vector along the direction.
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Which one of the following relations is true for Pauli matrices σx, σy and σz?
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σi(i = 1, 2, 3) represents the Pauli spin matrices. Which one of the following is not true?
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A particle is moving in a spherically symmetric potential V(r) = αr2, where α is a positive constant. In a stationary state, the expectation value of the kinetic energy of the particle is
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The commutator [Lx, y], where Lx is the x-component of the angular momentum operator and y is the y-component of the position operator, is equal to
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A beam of mono-energetic particles having speed v is described by the wave function (x) = u(x) exp(ikx), where u(x) is a real function. This corresponds to a current density
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There are only three bound states for a particle of mass m in a one-dimensional potential well of the form shown in the figure. The depth V0 of the potential satisfies
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A system in a normalized state with and representing two different eigen states of the system requires that the constants c1 and c2 must satisfy the condition
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In a hydrogen atom, the accidental or Coulomb degeneracy for the n = 4 state is
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A particle of mass m is represented by the wave function where k is the wave vector and A is a constant. The magnitude of the probability current density of the particle is
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