Nouredine Zettili. (Modified last on September 30, 2010). Note: This list of corrections pertains to: N. Zettili, Quantum Mechanics: Concepts and Ap- ...
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Sep 14, 2009 ... Corrections to the 7th printing, September 14, 2009. Introduction to Quantum Mechanics, 2nd ed. by David Griffiths. • page vii, last line of second paragraph: change “following” to “after fin- ishing”. • page 8, line 4: change x to j
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Corrections Quantum Mechanics: Concepts and Applications Nouredine Zettili (Modi…ed last on September 30, 2010)
Note: This list of corrections pertains to: N. Zettili, Quantum Mechanics: Concepts and Applications, (Chichester: John-Wiley, 2009); 2nd edition, ISBN: 978-0-470-02678-6 (Hardcover), 978-0-470-02679-3 (Paperback). Chapter 2 Page 151, replace Eq. (2.471) by ^2 H
=
2
(j
=
2
(j
1 ih 2 1 ih 1
j+j
2 ih 1
j+j
2 ih 2
j) (j j) ;
1 ih 2
j+j
2 ih 1
j)
Page 8, Page 151, replace Eq. (2.472) by (
2
^ 2 )2 H
=
(j
= j
1 ih 1
1 ih
1
j+j
j+j
2 ih 2
2 ih
2
j) (j
j=
1 ih 1 2 ^2
H :
j+j
2 ih 2
j)
Chapter 3 Replace Problem 3.5 and its solution on Page 196 by Problem 3.5 Assuming that the system of Problem 3.4 is initially in the state j 3 i, what values for the energy and the observable A will be obtained if we measure: (i)H …rst then A, (ii) A …rst then H? ^ and A^ are compatible. (b) Compare the results obtained in (i) and (ii) and infer whether H ^ ^ Calculate [H; A]j 3 i. ^ whose action on j n i is de…ned by Bj ^ ni = (c) Consider now an other operator B ^ nb0 j n+1 i. Repeat Questions (a) and (b) for the operator B. Solution
^ (a) (i) The measurement of H …rst then A is represented by A^Hj 2 ^ ^ Hj n i = n E0 j n i and Aj n i = (n + 1)a0 j n i, we have ^ A^Hj
3i
^ = 9E0 Aj
1
3i
= 36E0 a0 j
3 i:
3 i.
Using the relations (1)
(ii) Measuring A …rst and then H, we will obtain ^ Aj ^ H
^ = 4a0 Hj
3i
3i
= 36E0 a0 j
3 i:
(2)
^ and H ^ A^ yield the same result. (b) Equations (1) and (2) show that the actions of A^H ^ ^ This means that H and A commute; hence they are compatible. We can thus write ^ A]j ^ [H;
3i
= (36
36)E0 a0 j
3i
= 0:
(3)
^ Hj ^ (c) (i) The measurement of H …rst then B is represented by B 2 ^ ^ Hj n i = n E0 j n i and Bj n i = nb0 j n+1 i, we have ^ Hj ^ B
3i
^ = 9E0 Bj
3i
= 27E0 b0 j
3 i.
Using the relations
4 i:
(4)
4 i:
(5)
(ii) Measuring B …rst and then H, we will obtain ^ Bj ^ H
3i
^ = 3b0 Hj
4i
= 48E0 b0 j
^H ^ and H ^B ^ yield di¤erent results. This Equations (4) and (5) show that the actions of B ^ and B ^ do not commute; hence they are not compatible. We can thus write means that H ^ B]j ^ [H;
3i
= (48
27)E0 b0 j
4i
= 17E0 b0 j
4 i:
(6)
Replace the …rst two lines of Problem 3.11 on Page 204 by: Consider a system whose initial state j (0)i and Hamiltonian are given by 0 1 0 1 3 0 0 3 1@ A 0 ; H = @ 0 0 5 A; j (0)i = 5 0 5 0 4 where
has the dimensions of an energy.
Replace the third line from the bottom of Page 204 by: A measurement of the energy yields the values E1 =
5 , E2 = 3 , E3 = 5 ; the
Replace Eq. (3.222) on Page 205 by: p 2 2 j (t)i = e 5
