The Schrödinger equation for Li2+ is attatched. Briefly explain what each term in the equation represents.
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The Schrödinger equation for Li2+ is attatched. Briefly explain what each term in the equation represents.
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- Review schrodinger equations not dependent on 3D time in ball coordinates -V² + V(f) ) µ(F) = E Þ(*) 2m F = (r,0,9) and E is the energy system. Assume the potential is only radial function V (f) = V(r). With %3D 'To solve the Schrodinger equation above apply the method ψη, θ φ) -R(r)P (θ) Q (φ) variable separation problem : By defining the separation constant in the angular function 0 as (1 + 1) Also show that P(0) = P"(cos 0) angular function solution P(0) can be written as Polynomial Associated Legendre The combined angular functions of the sphere are known as the "harmonic function of the sphere" (spherical harmonics) Y(0, p) x Pi" (cos 0)e±imp3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.Q7B2
- The Bohr model predicts that the Hydrogen electron can only have allowed energies En where n2 n = 1,2,3,... and R>0 is a constant called the Rydberg energy constant. Explain briefly why the energy is negative and discuss the limit energy as n becomes large. S General\All Employees (unrestricted) * Accessibility: Good to go D. FocusReview schrodinger equations not dependent on 3D time in ball coordinates -v² + V(f) ) µ(F) = E Þ(*) 2m i = (r, 0, 4) V (f) = V(r). and E is the energy system. Assume the potential is only radial function To solve the Schrodinger equation above apply the method With y(r, 0, q) = R(r)P(0)Q(9) variable separation problem : Specify a common solution (r, 0,0) for l = 0 and V(r) = 0