Calculate (T) for a quantum mechanical harmonic oscillator using the following, normalized wavefunction. x² 4a³ V₁(x)=Axe A = ku ; απ π f=h² 8² 2μ όχι
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A: Mass of particle m = 9.109 × 10− 31 kg Width of the box a = 1.2 ×10− 10 m
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- Show 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.The normalized wavefunction is (1/4*pi*a^2) e^-(x^2)/(2a^2)For a quantum particle in a scattering state as it interacts a certain potential, the general expressions for the transmission and reflection coefficients are given by T = Jtrans Jinc R = | Jref Jinc (1) where Jinc, Jref, Jtrans are probability currents corresponding to the incident, reflected, and transmitted plane waves, respectively. (a). potential For the particle incident from the left to the symmetric finite square well -Vo; a < x < a, V(x) = 0 ; elsewhere, show that B Ꭲ ; R = A A
- [QUANTUM PHYSICS]= = An electron having total energy E 4.60 eV approaches a rectangular energy barrier with U■5.10 eV and L-950 pm as shown in the figure below. Classically, the electron cannot pass through the barrier because E < U. Quantum-mechanically, however, the probability of tunneling is not zero. Energy E U 0 i (a) Calculate this probability, which is the transmission coefficient. (Use 9.11 x 10-31 kg for the mass of an electron, 1.055 x 10-34] s for h, and note that there are 1.60 x 10-19 J per eV.) (b) To what value would the width L of the potential barrier have to be increased for the chance of an incident 4.60-eV electron tunneling through the barrier to be one in one million? nm(a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg. for each of the E₁ and E3 energy (b) Specify the degree of degeneracy levels, explaining your reasoning.