Calculate and plot the vibrational partition function of CSe2 between 500K and 1000K (with a step of 100K) given the wavenumbers 313 cm- (bend. two modes). 369 cm-1 ( symmetric stretch) and 1302 cm - (asymmetric stretch) assuming that each vibrational mode can be treated as a simple harmonic oscillator. Explain and discuss each step. (marks 10)
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- Problem Consider the ODE x = 2-3x with initial condition x(to) = 1 and to = 0. What is the value of the state x when t = 2? Estimate when the system will decay to a constant value using the time constant of the system (i.e., after 4 time constants)? 4Use your generic solution to the 2D box wavefunctions to demonstrate the following prop- erties of wavefunctions. 1. Show that if you independently normalize (x) and (y) that the product of (x) and (y) is also normalized. 2. Show that the wavefunctions for one dimension are orthogonal. Orthogonality means that f₁ Vndr = Smn, where the Kroenecker delta function means that the function is one for men and zero for m‡n. m 3. How many quantum numbers are needed to describe the energy of your system? 4. Show that the two dimensional wavefunctions are orthogonal by performing this test on the wavefunction for n = 1, ny = 2 and the wavefunction for nr = 2 and ny = 1. CLx Ly Mathematically the operations looks like f¹* f¹¹ V₁,2 (x, y) V2,1 (x, y) dxdy.# quantum mechanical particde in a harmonic osci lator potential has the initial wave function y,)+4,(x), where Y. and Y, are the real wavefunctions in the ground and fist exci ted state of the harmonic osciclator Hamiltonian- for Convenience we take mzhzw= 1 for the oscillator- What ở the probabilpty den sity of finding the par ticke at x at time tza?
- Question 3 Consider the simple and close-packed hexagonal direct lattices. (a) Find out the general expression for the structure factor for each lattice type. In this context, what is the significance of a complex structure factor? (b) Without resorting to the structure factor, determine in which structure(s) X-ray Bragg reflections arise from the lattice planes (0001), (0002), and (1010). Justify your answer by the use of the above determined structure factor or otherwise and explain the meaning of the four indices describing the above cited lattice planes.We will consider the Schrödinger equation in this problem as well as the analogies between the wavefunction and how boundary conditions are an essential part of developing this equation for various problems (situations). a) Write the form of the time-independent Schrödinger equation if the potential is that of a spring with spring constant k. Write the form of the time-dependent Schrödinger equation with the same potential. Briefly describe all the terms and variables in these equations. b) One solution to the time independent Schrödinger equation has the form Asin(kx). Why might it be called the wavefunction? If this form represents a wave of light, what is the energy for one photon? (Notek here stands for the wavevector and not the spring constant.) c) Why must all wavefunctions go to zero at infinite distance from the center of the coordinate system in all systems where the potential energy is always finite?Determine the wave function for n=1, l=0, ml=0 (variable separation equation), and derive the equation. (for the wave function phi use the differential equation, for the wave function tetha with the legendre polynomial equation, for the wave function R use the polynomileguare equation
- Needs Complete solution with 100 % accuracy. Don't use chat gpt or ai i definitely upvote you.Consider a thin hoop of mass (1.420 ± 0.001) kg and radius (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work. Please solve the uncertainty using the appendix I attached