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Consider the state where are the eigenstates of Value of is approximately ________ (Upto two decimal places)
An electron with energy 'E' is coming from far left to a potnetial step at x = 0. If E/V =9/8 then ratio of wavelength (λ_{1}/λ_{2}) of electron in region I and II is (Upto two decimal places)
Broshe wavelnegth
Wavefunction of a particle iii some one dimension potential is given by,
where k is the positive real constant. Probability of:finding the particle between x = 0 and x = a/4 is _____ %. (Upto two decimal places)
To find A, we have to normalize the wavefunction
Probability of finding particle between* = 0 and x = a/4
Consider the spin state of a system in reresentation
What is the average value of the operator corresponding to the xcomponent of the spin.
Find the eigenvalues of the component of spin operator of an electron in direction of a unit vector with spherical coordinates
Eigenvalves of the spin operator do not depent on direction They are always
An operator operates on a state vector such that is known to be existed, then
represent the total angular momentum operator. The value of is
A particle of mass m is being scattered by a potential given by V(r) = The differential crosssection calculated by Born's approximation is
differential cross section
Consider a particle in the 1D potential well given by
Now, a small perturbation is added to the well given as
The firstorder correction to the energy of second energy level, is
The wavefunction of the unperturbed second energy level is
First order correct to the energy.
In a twodimensional vector space spanned by basis vectors Two vectors in this space are given as
An operator is represented by matrix.
Wave function of a particle is given as If energy of particle in this state is and form of potential is then magnitude of the vector is _____ (upto two decimal places)
An electron is placed in an uniform magnetic field where points in the direction of vector The Hamiltonian of the system is H = is a constant and are pauli matrices Energy of ground state in terms of kB_{0}
A particle of mass 'm' with in box of length L, the wave function of the state is given by
then the energy of the particle of the state is
The given wave function,
Therefore, energy of the given state
A linear harmonic oscillator is perturbed by the potential V' (x) = ax^{2}bx^{4}; a and b constants. If first order energy correction to the second excited energy level is zero then in units of is (Upto two decimal places)
The wave function of a hydrogen atom is given by where 'a_{0}' is Bohr radius and is spherical harmonic function for l = 2 and m = 0. If probability of finding the electron is maximum at 'r_{mp}' and average distance between electron and proton is <r> then ratio of the two is (upto two decimal places)
It is clear from the wacefunction that n = 3.
spherical harmonics are orthonormal functions, so
Angular frequency for a wave propagating inside a waveguide is given in terms of the wave number K and the width of the guide b as
If group velocity is 3/4^{th} of the velocity then k is
Seven spin 3/2 identical noninteracting particle are subjected to the potential given as
The lowest energy of the system is
It is anisotropic harmonic oscillator
because of spin 3/2, maximum four particles can be filled in one energy level. Energies of two lowest energy levels are
A particle of mass 'm' in 1D harmonic oscillator potential In the nonrelativistic limit, where the kinetic energy T and momentum P are related as T = p^{2}/2m. The ground state energy is known to be For the relativestic corrections in relation between T and P, calculate energy shift in ground state to the order of 1/c^{2} (c is speed of light in vacuum)
Kinetic energy (T) = E  mc^{2}
The wave function of a onedimensional system is given as
where A, n and a are positive constants. The form of the potential if V(x) → 0
The wavefunction of a hydrogen atom is given by
where a_{0} is Bohr radius and is spherical harmonic function for l = 1 and m = 0. What is the dispersion in the measurement of distance of electron from nucleus?
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