A particle with mass m is in the state „2 mx +iat 2h ¥(x, t) = Ae where A and a are positive real constants.
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- How to solve this questionSuppose that ak > 0 for all k e N and E ak < 0. For each of the following, prove that the given series converges. ak ( a ) ΣΕΙ 1+ k3ak (b) Lk=1 1+ ak Vak (c) Ek=1 k < 0o.3. The classical partition function of a gas of noninteracting indistinguishable particles is written as exp{- N! 2m Z= where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x³xdx = Va Hint:
- Consider the following measurements of a mass and speed for an object using the formula determine the momentum uncertainty of the object. Express answer in g•m/s Suppose Fuzzy, a quantum-mechanical duck, lives in a world in which h = 2 J s. Fuzzy has a mass of 1.90 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the duck's speed? m/s (b) Assuming this uncertainty in speed to prevail for 4.90 s, determine the uncertainty in Fuzzy's position after this time. mA proton is accelerated to a speed of 2.10*10E5ms. If the uncertainty in the measured speed is 5% what is the mimum uncertainty in the position of the proton?
- An atom is in an excited state for 4.00 us before moving back to the ground state. Find the approximate uncertainty in energy of the photon in units of 10¹¹ eV. (A) 8.23 (B) 3.78 (C) 4.97 (D) 5.49 (E) 6.17This problem is designed to give you practice using the Dirac delta function. Eval- uate the following integrals. Show your reasoning.