Given the situation below, use 1st order perturbatin theory to estimate the ground state energy.
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Given the situation below, use 1st order perturbatin theory to estimate the ground state energy. 0a/3...
(a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b) Calculate the energy shift in the ground state and in the degenerate 1t excited state of a 2-dimensional harmonic oscillator H(P2P,2/2m m(x +y)due to the perturbation V 2Axy. (20 pts) (a) Use the variational method to estimate the ground state energy of a particle of |mass m in a potential Vx)kx, k > 0. (b)...
Consider a system with energy levels quantized as in the figure given. Ground state is -10eV, 1st exited state is -8 eV, 2nd exited state is -3 eV and finally 3rd exited state is -1 eV. A.) What is the change in energy (eV) of the system if it absorbs a photon and system moves from ground state to 3rd exited state? B.) What is the change in energy (eV) of the system if it absorbs a photon and system...
Use the variational principle to estimate the ground state energy of a particle in the following potential: V=cx for x>0 and V=infinity for x<0 Use Dxe^-ax as your trial function and minimize as necessary with respect to a. Assume the constant c is real and greater than zero
Solve 1st one asap At a given temperature the rotational states of molecules are distributed according to the Boltzmann distribution. Of the hydrogen molecules in the ground state estimate the ratio of the number in the ground rotational state to the number in the first excited rotational state at 300 K. Take the interatomic distance as 1.06 Å. Estimate the wavelength of radiation emitted from adjacent vibration energy levels of NO molecule. Assume the force constant k-1,550 N m In...
1. MO theory for homonuclear diatomic molecules (a) Determine the ground state electron configuration of the C2 anion. (1 points) (b) Calculate the bond order of the C2 anion. Is its dissociation energy greater or smaller than that of C2? Is its bond length greater or smaller than that of C2-(3 points) (c) Use MO theory to explain why the dissociation energy of the N is less than that of N2, but the dissociation energy of O is greater than...
Using the first order of perturbation theory, find the corrections to the ground state (1S) and state 2S of a hydrogen atom due to the finite size of the nucleus. Consider the nucleus be a sphere of radius R with uniformly distributed charge e.
09 Estimate the ground state energy and wavefunction for a particle in a box using the variational method with the following trial wavefunction, where N is the normalization constant and ß is a variational parameter that should be minimized. 14) = N exp(-Bx2) (7.6) 1. Is this a good trial wavefunction for this approximation (justify your answer)? 2. Why is this not a good wavefunction? 3. Can you solve this problem both analytically and numerically? Pay careful attention to limits...
Estimate the ground-state energy of a one-dimensional simple harmonic oscillator using (50) = e-a-l as a trial function with a to be varied. For a simple harmonic oscillator we have H + jmwºr? Recall that, for the variational method, the trial function (HO) gives an expectation value of H such that (016) > Eo, where Eo is the ground state energy. You may use: n! dH() ||= TH(c) – z[1 – H(r)], 8(2), dx S." arcade an+1 where (x) and...
energy Use this diagram to complete the table below. Which is the ground state? (pick one): How many excited states are there? How many lines are in the absorption line spectrum? Which transition causes the emission line at the shortest wavelength? 0-0 Which transition causes the emission line at the longest wavelength? Explanation Check
Below is the frequency response of a dynamic system +)20 20 → 1st order 40">2"d Order a. What are the corner frequencies? 、.a.,.1D.歩100 b. How many poles in the system? e. How many zeros in the system'? d. For the input signal shown in the Figure below find (at steady-state situation): i. The output signal amplitude ii. The output signal phase (in degrees and show the sign)... Plot the output signal on the Figure below e. 57 58 9 61...