Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
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Chapter 9, Problem 9.18P

(a)

To determine

The energy of the ground state, measured up from the bottom of the well.

(b)

To determine

Introduce a perturbation H'=αx and sketch the total potential and note that the particle can now tunnel out.

(c)

To determine

The tunneling factor γ and the time it would take for the particle to escape.

(d)

To determine

The value of τ and compare it to the age of the universe.

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PROBLEM 2. Consider a spherical potential well of radius R and depth Uo, so that the potential is U(r) = -Uo at r R. Calculate the minimum value of Uc for which the well can trap a particle with l = 0. This means that SE at Uo > Uc has at least one bound ground state at l = 0 and E < 0. At Ug = Uc the bound state disappears.
Problem # 2. In the two-level system, estimate the emission line full width at half maximum (FWHM) for spontaneous emission at 650 nm if the spontaneous radiative lifetime of the upper state is about 3,000 nanoseconds.
Could someone explain to me in detail why bringing a crystal substance to absolute zero isn't possible? I know it's not because of quantum mechanics and uncertainty like some people say, because particals at their lowest zero-point will have a temperature of exactly 0 K, even though they're still experiencing motion.  From what I've gathered, the energy or time required to pull it off is infinite, but I can't find any equations or clear explanations as to why or how that is. And I also don't know if there's any other reasons beyond that. If you could give me a thourough a breakdown for how absolute zero is impossible as you possibly could, I'd greatly appreciate it. Take as much extra time as you need. As long as it's detailed and correct I'm happy. Though ideally I would before it come in before the end of the day.
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