Quantum phenomena are often negligible in the “macroscopic" world.Show this numerically for the following cases:(a) The amplitude of the zero-point oscillation for a pendulum of length1 = 1 m and mass m = 1 kg.(b) The tunneling probability for a marble of mass m = 5 g moving at aspeed of 10 cm/sec against a rigid obstacle of height H = 5 cm and widthw = 1 cm.(c) The diffraction of a tennis ball of mass m = 0.1 kg moving at aspeed v =0.5 m/sec by a window of size 1 × 1.5 m².

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Answered: Quantum phenomena are often negligible…

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An electron has a kinetic energy of 13.3 eV. The electron is incident upon a rectangular barrier of height 21.5 eV and width 1.00 nm. If the electron absorbed all the energy of a photon of green light (with wavelength 546 nm) at the instant it reached the barrier, by what factor would the electron's probability of tunneling through the barrier increase?
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= = 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
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Determine the expectation values of the position (x) (p) and the momentum 4 ħ (x)= cos cot,(p): 5V2mw 4 mah 5V 2 sin cot 2 ħ moon (x)= sin cot, (p)= COS at 52mo 2 4 h 4 moh (x)= 52mo sin cot.(p) COS 2 h s cot, (p) 5V2mco 2 moh 5V 2 sin of as a function of time for a harmonic oscillator with its initial state ())))
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