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1 Evaluate 2 Evaluate 8x28z a³ [2x cos(y) + exp(xy - 2...

1 Evaluate 2 Evaluate 8x28z a³ [2x cos(y) + exp(xy - 2°)] 3 Solve the system of equations 3x + 4y + 2z = 9 x - 6y + 2z = 6 -3x - 2y - Z = 6 for x, y, and Z. 4 Evaluate 3 4 2 det 1 -6 2 . (2.1) -3 -2 -1 5 Consider a pyramidal structure with a pentagonal base as shown in Fig....

1. Consider a system of N heterodiatomic molecules weakly ab...

1. Consider a system of N heterodiatomic molecules weakly absorbed on a surface. Assume they do not interact with each other (two-dimensional ideal gas). The energy levels for planar rotation are Ej = 21 2 , where J = 0,1,2, and I is the moment of inertia for rotation of the molecule. The degen...

1) In the class #26 & #27 handout I used the variati...

1) In the class #26 & #27 handout I used the variational method to calculate the expression for the energies of two MO that were constructed as linear combinations of two non-equivalent AO. a) Consider the Molecular orbitals that would be obtained from mixing two non-equivalent AO: chlorin...

Provide answers to the following questions on separate paper...

Provide answers to the following questions on separate papers and attach to this problem sheet. Please write your answers clearly. 1. (6 pts) Prove that the following wave function is an eigenfunction of i2 and find the eigenvalue. Determine whether this is an eigenfunction of L2 = to as well. =...

Periodic motion: 11-1 The general equation of simple harmon...

Periodic motion: 11-1 The general equation of simple harmonic motion, x = A cos(wt + 00), can be written in the equivalent form x = B sin wt + C cos cot a) Find the expressions for the amplitudes B and C in terms of the amplitude A and the initial phase angle Oo. b) Interpret these expressio...

Provide answers to the following questions on separate paper...

Provide answers to the following questions on separate papers and attach to this problem sheet. Please write your answers clearly. 1. (6 pts) For the operator Â and function f shown below, determine whether f is an eigenfunction of A or not. If f is an eigenfunction, find out the eigenvalue...

2. (14 pts) A quantum particle with unit mass (m = 1) is in ...

2. (14 pts) A quantum particle with unit mass (m = 1) is in a one dimensional box where the potential energy, V (x) = o for o < x < 2 and V (x) = 80 otherwise. Answer the following questions. (a) (6/14) Prove that on(x) = sin ( NTT ), n = 1,2, 2 is an eigenfunction of the Hamilt...

Ionization Potentials The ionization potentials of molecule...

Ionization Potentials The ionization potentials of molecules can be estimated in two different ways: by means of Koopmans theorem or by direct computation of the difference between the molecule and its corresponding cation. Set up input files to perform geometry optimizations of CH4, NH3, H2O, and...

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