Answered: The radial Hamiltonian of an isotropic… | bartleby

Related questions

Question

The radial Hamiltonian of an isotropic oscillator ((1 = 0) is
ħ² d (r² 2/1 ) + 1/ / mw² p²
2mr² dr
dr
Estimate the ground state energy level of the atom using variational method with the trial function
&
= e
ar

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 11 images

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

da=do= 4) For the following d hydrogenic wavefunctions, find the magnitude and the z component of the orbital angular momentum. You can give your results in terms of h. اور اہل = 1 √2 16t i√2 i√2 Final (d₁2+ d_2) = (165) R₁2(r) (x²- y²)/r² 151/2 1/2 R₁2(r) (3cos²0-1)=(16) R2(1)(32²-7²)/² 1/2 (d+2-d-2)= (15) Rm2(7)xy/² =(d. 1+d-1)= (d_1-d-1)=- 1/2 1/2 (15) R₁2 (r)yz/r² 10 June 2011 1/2 (45) * Ru2(1) 2x/r²
A quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)
(a) What is the magnitude of the orbital angular momentum in a state with e = 2? (b) What is the magnitude of its largest projection on an imposed axis? (a) Number 2.50998008 Units J.s (b) Number 2.11 Units J.s
An electron occupying the n = 6 shell of an atom carries z-component orbital angular momentum = (–2) × h/2π. Given that the electron’s total orbital angular momentum is x × h/2π, what is the minimum possible value of number x(remember to use the scientific notation)?
If we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?
(d) The following orbital belongs to the 3d subshell of the Hydrogen atom: r Y(r, 0, 0) = A(Z) θ, φ) 2 r e 3ao sin² (0) e²i зао where A and ao are constants. Using the operator for the z-component of orbital angular momentum (L₂ = -ih d/do) determine the m, for this particular orbital. (e) Consider the wavefunction, r r Y(r,0,0) = A-e 2do cos(0) do (i) Identify the radial part of this orbital function and the number of radial nodes. (ii) Identify the angular part of the orbital function and the number of angular nodes. Z (iii) Using this information and the L₂ = -ih d/do operator obtain the n, 1, and, m quantum numbers and identify the orbital.
A researcher observes hydrogen emitting photons of energy 1.89 eV. What are the quantum numbers of the two states involved in the transition that emits these photons?
24. Consider a modified box potential with V(x) = V₁x, Vi(ar), x a Use the orthogonal trial function = c₁f₁+c₂f₂ with f₁ = √√sin (H) and f2 = √√ √√sin sin (2) to determine the upper bound to ground state energy.