Consider a two state system with normalized energy eigen state ψ1 & ψ2 and energy E1 < E2 what is the possible range for the expectation value of on an orbitrary linear combination of two state
Suppose a wave function and an operator is given by is given by
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Consider the following Stem-Gerlach apparatus incoming beam consist of electron 2/3 of them having spin and other 1/3 have spin in the z-direction
what fraction of the incident beam are detected in the up and down outputs of the apparatus
Consider a system whose initial state at r = 0 is given in term of a complete and orthonormal set of three vectors as follows the probability of find tlie system at tune t in state is _______ (upto two decunalplaces)
An election is confined in an infinite square well of width 10x10^-15 m. Calculate the wavelength of the electron emitted when the proton undergoes a transition from the first excited state (n=2) to the ground state (n=1).
Consider a tliree dimensional harmonic oscillator with Hamiltonian
The number of distinct eigenstates with energy eigenvalue 5/2 ℏω is_________
(Answer should be an integer).
Consider an operator for a system of total angular momentum j = 1 then winch of the following state having non zero uncertainty
In the simple harmonic oscillator
what are the condition on m and m' for to be non-zero
Find the differential cross-section for die scattering of slow (low velocity) particle from a spherical delta poten- tial V (r) = V0 δ (r - a)
For case of n = 2, ℓ = 1, m = 0 the value of r at which the radial probability density of the hydrogen atom reaches its maximum is ____ a0. (answer should be an integer)
Consider a system winch is mtially in the state was measured with value -ℏ, the probability is_______(upto one decimal place)
An electron is confined in the ground state of a one dimensional harmonic oscillator such that energy required to excite to its first excited state is _____ (MeV)
A particle of mass m coming in from the left with energy E > 0, encounters barrier potential
The wave function is given by
The constant A and B satisfy which one of the following relation?
Calculate the width of the probability density distribution for r(i.e Br) for hydrogen atom for the state
At t = o, a state is given by
Where are ortlionomial stationary states of energy El & E2 respectively with E2 > El what is the shortest tune T > 0 for w hich is orthogonal to
If the state of a particle moving in one dimensional harmonic oscillator is given by
Where represent the normalized nth energy eigenstate find the expectation value of number operator
A particle of mass m moves in a one dimensional potential box
Consider the V0 part as perturbation, using first order perturbation method calculate the energy of ground state.
A spin state precesses in a magnetic field same way as the classical magnetic dipole precesses in magnetic field with lasmor frequency given by consider the Hamiltonian Larrnor frequency is (in tem is of ω0)
(answer should b e an mteger)
Consider a system of four non-interacting identical spin 1/2 particles that are in same state and confined to move in a one-diniension infinite potential well of length a: V(x) = 0 for 0 < x < a and V(x) = ∞ forotlier values of x. The ground state energy of the system in units of is (answer should be an integers).
Consider a system whose intial state and hamiltonian are given by
find the total energy of a system
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