Answered: calculate the expectation value for the… | bartleby

Related questions

Question

calculate the expectation value for the potential energy of the H atom with the electron in the 1s orbital. Compare your result with the total energy. What is the kinetic energy of H atom in this state? Verify the virial theorem for the Coulomb potential.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

In the following questions, we will use quantum states made up of the hydrogen energy eigenstates: Q1: Consider the election in a hydrogen atom to initially be in the state: F A. B. C. a) What is the probability of measuring the energy of this state and obtaining E₂? √3 √ vnim (r0,0)=R(r)Y," (0,0) always Y(t = 0) = √3 R₁OYO at t=0 but something different at t>0 ² at t=0 but something different at t>0 D. always 3 + E. Something else. b) Explain your answer. R₂₁ + R32Y₂¹
could you also explain to me how you come up with question A?
A rectangular corral of widths Lx = L and Ly = 2L contains seven electrons. What is the energy of (a) the first excited state, (b) the second excited state, and (c) the third excited state of the system? Assume that the electrons do not interact with one another, and do not neglect spin. State your answers in terms of the given variables, using hand me (electron mass) when needed.
provided a system of 2 electrons in a one-dimensional box, write the approximate wavefunctions including the spin (but without considering interelectronic repulsion) for the states with an electron with n=1 and an electron with n=2. State which of the resulting states has the lowest energy. Symbolically build the linear combinations of the wavefunctions products (including spin). SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAY
O Consider the kinetic energy matrix elements between Hydrogen states (n' = 4, l', m'| |P|²| m -|n = 3, l, m), = for all the allowed l', m', l, m values. What kind of operator is the the kinetic energy (scalar or vector)? Use this to determine the following. For what choices of the four quantum numbers (l', m', l, m) can the matrix elements be nonzero (e.g. (l', m', l, m) (0, 0, 0, 0),...)? Which of these nonzero values can be related to each other (i.e. if you knew one of them, you could predict the other)? In this sense, how many independent nonzero matrix elements are there? (Note: there is no need to calculate any of these matrix elements.)
Write down the confi gurations for the ground states of calcium and aluminum. What are the LS coupling quantum numbers for the outside subshell electrons? Write the spectroscopic symbol for each atom
Write down the partition function for this system. What's the probability of finding the atom in its ground state, if e/kT = In (3)? Assume now that the atom has a second excited state that's 9-fold degenerate and has energy 26. What's the probability of finding the atom with energy E = 2ɛ, again
1.The odd parity eigenstates of the infinte square well , with potential V = 0 in the range −L/2 ≤ ? ≤ L/2, are given by : (see figure) and have Ψn(x, t) = 0 elsewhere , for n=2 , 4 , 6 etc a) Sketch the potential of this system , including in your sketch the positions of the lowest three energy levels . Indicate in your sketch the form of the wavefunction for a particle in each of these energy levels , and state which of the wavefunctions you have drawn could be decirbed by the Ψn written above (see figure) . b) Calculate the expectation value of momentum , ⟨p⟩ for a particle with n=2 c) Calculate the expectation value of momentum squared ⟨p 2⟩ , for a particle with n = 2 . Hint : you may use the mathematical identiy sin2 x = 1/2 (1 − cos 2x) without proof .