The Schrödinger equation is +U(x)\» = E¼. 2m dx? Starting from the left, identify each term in the equation.
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- not sure why the mass is incorrect please helpShow that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.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. 2m
- The difference in energy between allowed oscillator states in H2O molecules is 0.454 eV. What is the oscillation frequency (in Hz) of this molecule? HzL What are the differences and similarities between the quantization of angular momentum in the Bohr model and the Schrödinger theory? Explain in your own words and use examples from both to support your explanation. 111 Responses Reply Showing All Responses ordered by Newest ResponsesThe L series of the characteristic x-ray spectrum of tungsten contains wavelengths of 0.1099 nm and 0.1282 nm. The L-shell ionization energy is 11.544 keV. Which x-ray wavelength corresponds to an N → L transition? Determine the ionization energies of the M and N shells: If the incident electrons were accelerated through a 40.00 keV potential difference before striking the target, find the shortest wavelength of the emitted radiation:
- Clearly explain why the quantum oscillator is a good model for representing molecular vibrations.For a given value of l , what are the allowed values of ml ? What are the allowed values of ml for a given value of n ? Give an example in each case.An electron is in a three-dimensional box. The xx- and zz-sides of the box have the same length, but the yy-side has a different length. The two lowest energy levels are 2.18 eVeV and 3.47 eVeV, and the degeneracy of each of these levels (including the degeneracy due to the electron spin) is two. What is the length LY for side of the box? What are the lengths LXLX, LZLZ for sides of the box? What is the energy for the next higher energy state? What are the quantum numbers for the next higher energy state? What is the degeneracy (including the spin degeneracy) for the next higher energy state?