1. Explain the variational principle and illustrate it with some example (different from the one in...
Exercise 7: Variational principle and hydrogen atom a) Variational method: show that EOT OTHOT)orloT) yields an upper bound to the exact ground state energy Eo for any trial wave function r. b) Apply the variational method to the ground state of the hydrogen atom (without rel- ativistic corrections), using as trial function r Ce"ar and compare it to the result of problem 7.13 of the book. c) The variational method can also be applied to excited states, by taking care...
Two students have a very pressing homework deadline concerning the application of the variational principle to estimate the ground state energy of the harmonic oscillator. The Hamiltonian operator of such system is î H -12d = 24 d.22 + 2 .2. in which u is the reduced mass of the oscillator and w = (force constant/u)/2 its natural frequency. The correct energies for this system are well known Eo = (v +) , v= 0,1,2, ... As the trial function...
Can someone please help me understand question 2? I understand the first one, but for some reason I keep getting the second one wrong In the class lecture notes, the result of the first-order perturbation calculation for the energy of lithium was given as E" - 2J12+ILL-K2. This energy is added to the EC value obtained by treating each electron as if it were in an independent hydrogen-like orbital in order to estimate the total energy of the lithium atom....
2. In the derivation of the energy levels in the hydrogen atom one commonly assumes that the nucleus is a point charge. However, in reality the size of the nucleus is of the order of Im = 10-15m. Since this is very much smaller than the typical distance of the electron from the nucleus, which is of the order of a0-0.5A = 0.5 × 10-10m, the finite size of the nucleus can be taken into account perturbatively. (a) Assume that...
2). Rough estimation of the diameter of an aluminum atom: Given aluminum density as p-2.7*10 kg/m', atomic weight is 27 (i.e. the mass of 1 mole of aluminum atoms is 27g. Imole 6.02x10 ). Assume atoms of aluminum metal are spherical with spaces in between the aluminum atoms take up 74.1% of the volume of the material. What is the diameter of an aluminum atom? (Note: Volume of a sphere with radius ris: V-(4/3)xr) 4. (20") (1). In E-beam lithography,...
I.(20p) Fill the following spaces with or circle the appropriate answers (can be more than one!). I.1. In Tom's frame of reference, two events A and B take place at different locations along the x axis but are observed by Tom to be simultaneous. Which of the following statements is true? (1) No observers moving relative to Tom will find A and B to be simultaneous, but some may see A before B and others B before A. (2) No...
1. According to the paper, what does lactate dehydrogenase (LDH) do and what does it allow to happen within the myofiber? (5 points) 2. According to the paper, what is the major disadvantage of relying on glycolysis during high-intensity exercise? (5 points) 3. Using Figure 1 in the paper, briefly describe the different sources of ATP production at 50% versus 90% AND explain whether you believe this depiction of ATP production applies to a Type IIX myofiber in a human....