eigen values is E1 /4
eigen value is
b) [H] energy is a sharp observable as is an eigen function of the operator. The expected value is the energy is eigen value E1 /4 nd the uncertainty is 0
c)
the eigen value is is is sharp observable. Uncertainty is 0, expected vlue of z-component is the eigen value
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
A hydrogen atom is in the n = 6 state. Determine, according to quantum mechanics, (a) the total energy (in eV) of the atom, (b) the magnitude of the maximum angular momentum the electron can have in this state, and (c) the maximum value that the z component Lz of the angular momentum can have.
Find the expectation value and uncertainty of the z component of the angular momentum Lz for an electron in an hydrogen atom( in any state) You can take the operator Lz to be Lz = -i / psi
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
Exercise 1: The helium atom and spin operators 26 pts (a) Show that the expectation value of the Hamiltonian in the (sa)'(2a)' excited state of helium is given by E = $42.0) (Avo ) anordes ++f63,(-) (%13-12 r) 62(e)drz + løn.(r.) per 142, (ra)]" drų dr2 - / 01.(ru) . (ra) Anemia 02.(r.)61.(r.)dr; dr2 (1) Use the approximate, antisymmetrized triplet state wave function for the (Isa)'(280)' state as discussed in class. Hint: make use of the orthonormality of the hydrogenic...
An electron in a sodium atom is in the M shell. Determine the maximum value the z component of its angular momentum could have. (Use the following as necessary: ?.) Lz = ____?
An electron in a sodium atom is in the P shell. Determine the maximum value the z component of its angular momentum could have. (Use the following as necessary: h.) Lz
A particle on a sphere is described by the state function Ψ = N {1 + cos(θ)} Find a) the value of the normalization constant N b) the expectation value of the energy E c) the possible values of the z component of angular momentum (Lz) that might be measured, and which of these possibilities is most likely.
Problem 3. At some moment of time, an electron in the hydrogen atom is prepared in the state y=1/12(R21Y1-11T>+ R32Y2011>). Determine the expectation values of (a) Î, Îz - the square of the orbital angular momentum and its projection on the z-axis, (b) Ŝ2, S2 - the square of the spin and its projection on the z-axis, (c) ſ2 = (Î + Ŝ2 - the square of the total angular momentum. Do not use calculus, use algebra in this problem.