1. Show that for n=1, the probability of finding the harmonic oscillator in the classically forbidden region is 0.1116. Using a physically motivated argument, discuss whether then = 10 level will be more, equally or less likely to be found in the classically forbidden region than a harmonic oscillator in the n= 1 state.
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- 4-7 ) please Solve All of it .3.) A classical ball bounces back and forth between two rigid walls with no loss of speed. After a long time has passed, the ball's position is measured at a random time. a. Is the probability Prob(inA)that the ball is found in sectionAlarger than, smaller than, or the same as the probability Prob(in B) of being found in section B?help with modern physics
- Two identical non-interacting particles of rest energy 0.1973 MeV are trapped in the same infinitely deep one-dimensional square well of width 0.625 µm . If the total energy of the two-particle state is 0.31568 ueV, write down the two-particle wave function in each of the following cases: 1. the particles are spinless; 2. the particles are electrons and the spin of the state is s = 0; %3D 3. the particles are electrons and the spin of the state is s = 1; %3D 4. When the Coulomb repulsion between the electrons is taken into account in 2 and 3 , which spin state will have the lower energy?Choose the correct answer!. 1. The wavelength associtated with a particle in • 2-D box of length I is 2.L L @ © n n 2n Ju • 2. At boundary Condition @√(x) is always continuous except © Vcx = constant. where 9x 16₁ VCX) = 0 = 00 3. The Zero Point energy of the 1-dimensional box occurred with @n=1 n=0 ©n=30 4- In the eigen value equation, the eigen Values is determined by : @Operatory Only Condition ony by boundry by Operatory plus. the boundary conditions4. Find the points of maximum and minimum probability density for the nth state of a particle in a one- dimensional box. Check your result for the n=2 state.
- 6Assume an electron moves in one dimensional infinite potential box its width L= 6nm, theni) Draw the energy level diagram and determine the value of this energy for the three first energy states.ii) Plot and explain the wave function for n= 1, 2, 3 states.iii) Sketch and explain the probability distribution of the electron for n=2 and n=3 states.iv) Mark on the figure the probability of finding the electron between x= L/3 and 2L/3 for n= 3 state.Chat gpt means downvote
- 4. Consider the two-time position correlation functions, C(t)= (X(t)x(0)), where X(t) is the position operator in the Heisenberg picture. Evaluate this function explicitly for the ground state of a one-dimensional quantum harmonic oscillator.. (1) Find the kinetic, potential and total energies of the hydrogen atorn in the 2nd excited level.2.) An electron is in the n = 1 state in a hydrogen atom. а.). Write down the radial wavefunction. b.) Write down the radial probability density. с.) Find the mean radius. You may use the fact that lim,→. x"e¯* = 0. X→∞ d.). Find the mean value of r². e.) . "Find the standard deviation of the radius. The answer is between a, and ao.