3. A particle is confined to x-axis the between x = 0 and x = L. The wave function of the particle is = Ae (¹) with A E C. Determine A. Determine (p). Determine (E). a. b. C.
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A: The detailed solution is following.
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- 3. 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.4. Show that the wave functions for the ground state and first excited state of the simple harmonic oscillator, given by W0 (x) and W1 (x), are orthogonal, where %(x) = Aoe¬max² /2h 4 (x) = A1V m@ -mox² /2h -xeOne of the series in the line spectrum of atomic hydrogen is the Brackett series. The lines in this series are produced when the electron makes transitions into the n = 4 level from higher excited states. What is the second longest wavelength in this series? a.4.65 × 10-6 m b.2.63 × 10-6 m c.3.81 × 10-4 m d.2.63 × 103 m e.3.81 × 105 m