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Is it because when multiples of 2n /a are added to, or subtracted from, the wave vector, the movement of the atoms in the chain remains the same?
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- 2² $2(x)] where $1(x) and ø2(x) are The wave function is given by y (x, t) = C[3e¬iwitp1(x) + 4e-iwzt, energy eigenfunctions that are orthonormal, and w1 = 3.0 × 1015 Hz and w2 = 7.5 × 1015 Hz. What are the two energy levels in units of eV? Calculate the average energy of the system in eV.(5) The wave function for a particle is given by: (x) = Ae-=/L for r 2 0, where A and L are constants, and L > 0. b(x) = 0 for r < 0. (a) Find the value of the constant A, as a function of L. A useful integral is: fe-K=dx = -ke-K, %3D where K is a constant. (b) What is the probability of finding the particle in the range –10 L < x< -L? (c) What is the probability of finding the particle in the range 0Are these acceptable wavefunctions in the range x = -infinity to infinity? If so, please explain. cos kx x-1/44 (X) = Ne-a lxl Normalize the function (Step by step)4. Show that the wave functions for the ground state and first excited state of the simple harmonic oscillator, given by W0 (x) and W1 (x), are orthogonal, where %(x) = Aoe¬max² /2h 4 (x) = A1V m@ -mox² /2h -xe500 neutrons freely moving inside box his walls is x=0 and x=L, if the wavefunction of every neutron at time 0 is p(x) = Ax(L + x²) a- find the normalization constant A b- calculate the average of the kinetic energy (T) of each neutron in range 0