a) Consider three operators A, B and Ĉ. Assume that they obey the following commutation relations [4,Ĉ]=iß [B,Ĉ]= iÀ A(AB)A(C) 2(À² +. Show that b) For a 1-dimensional system with general Hamiltonian H +V(x) 2m = d{xp) find dt Express your answer in terms of x, p and V . c) Using the relativistic relation between mass and energy E= mc² write down an uncertainty relation for mass and time. Assume that a free neutron has a life time of ~10° s. Estimate the uncertainty in the neutron's mass.

a) Consider three operators A, B and Ĉ. Assume that they obey the following commutation relations [4,Ĉ]=iß [B,Ĉ]= iÀ A(AB)A(C) 2(À² +. Show that b) For a 1-dimensional system with general Hamiltonian H +V(x) 2m = d{xp) find dt Express your answer in terms of x, p and V . c) Using the relativistic relation between mass and energy E= mc² write down an uncertainty relation for mass and time. Assume that a free neutron has a life time of ~10° s. Estimate the uncertainty in the neutron's mass.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

a) Consider three operators A, B and C. Assume that they obey the following commutation
relations
[4‚Ĉ]= iß
[B,Ĉ] = iÀ
1
A(AB)A(C)2(À² + B*)
Show that
2
b) For a 1-dimensional system with general Hamiltonian H
+V(x)
2m
d(xp)
find
dt
Express your answer in terms of x, p and V .
c) Using the relativistic relation between mass and energy E = mc² write down an uncertainty
relation for mass and time.
Assume that a free neutron has a life time of ~10ʻ s. Estimate the uncertainty in the neutron’s
mass.

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