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 2.4, Problem 2.17P
To determine

The proof that [Aeikx+Beikx] and [Ccoskx+Dsinkx] are equivalent ways of writing same function of x.

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The first four Hermite polynomials of the quantum oscillator areH0 = 1, H1 = 2x, H2 = 4x2 − 2, H3 = 8x3 − 12x.  Let p(x) = 12x3 − 8x2 − 12x + 7. Using the basis H = {H0, H1, H2, H3}, find the coordinate vector ofp relative to H. That is, find [p]H. This is a textbook question, not a graded question
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.
For a system of bosons at room temperature, compute the average occupancy of a single-particle state and the probability of the state containing 0, 1, 2, or 3 bosons, if the energy of the state is 1 eV greater than μ
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