Show that the following function Y(0,9)= sin 0 cos 0 e=º is the solution of Schrödinger 1 sin 0 21 sin 0 de Y(0,9)= EY (0,9) and find the equation: sin? 0 dg energy, E.
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- Complete the derivation of E = Taking the derivatives we find (Use the following as necessary: k₁, K₂ K3, and 4.) +- ( ²) (²) v² = SO - #2² - = 2m so the Schrödinger equation becomes (Use the following as necessary: K₁, K₂, K3, ħ, m and p.) 亢 2mm(K² +K ² + K² v k₁ = E = = EU The quantum numbers n, are related to k, by (Use the following as necessary: n, and L₁.) лħ n₂ π²h² 2m √2m h²²/0₁ 2m X + + by substituting the wave function (x, y, z) = A sin(kx) sin(k₂y) sin(kz) into - 13³3). X What is the origin of the three quantum numbers? O the Schrödinger equation O the Pauli exclusion principle O the uncertainty principle Ⓒthe three boundary conditions 2² 7²4 = E4. 2mda=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/r²An experimenter wants to separate silver atoms in a Stern-Gerlach experiment by at least 1 cm (a large separation) as they exit the magnetic fi eld. To heat the silver she has an oven that can reach 1000°C and needs to order a suitable magnet. What should be the magnet specifi cations (magnet length and magnetic fi eld gradient)?
- The normalized time independent wavefunction for an electron in an infinite square well potential in the nh quantum state is given by, 2 плх w,(x)=, -sin n = 1, 2, 3, .. L L If L= 0.250 nm, use the Hamiltonian operator (with V = 0) to find the energy for n = 10. h = 6.626 x 1034 J-s 1 eV = 1.6022 x 10-19 J Given: m. = 9.1094 x 1031 kgThe expectation value,Calculate the probability that for the 1s state the electron lies between r and r+dra 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.An electron is in an infinite potential well of width 364 pm, and is in the normalised superposition state Ψ=cos(θ) ψ5-sin(θ) i ψ8. If the value of θ is -1.03 radians, what is the expectation value of energy, in eV, of the electron?