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Quantum Mechanics Homework: Spin States and Probability Calculations, Assignments of Quantum Mechanics

University of Colorado Boulder (CU Boulder)Quantum Mechanics

This is homework three for quantum mech

Typology: Assignments

2022/2023

Uploaded on 12/18/2023

connor-riley
connor-riley 🇺🇸

2 documents

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bg1
Homework
IF
2
PnSlem#
14.7
=
¥
It
>
-
Es
I
-3
142
)
=
¥
It
)
f
Es
I
-7
1437
=
#
It
>
-
ea
'
l
-
s
a)
Call
the
orthogonal
,
normalized
vector
147
=
a
(
t
)
t
b
I
→
Now
require
of
107--1
and
<
4147--0
󲰛
54
,
14,7
-
-
Ca
's
tl
this
-
D
#
t
)
-
EH
=
a
*
Fs
-
b
*
⇐
=
O
󲰛
a
=
2b
24
,
14,7
-
-
lat
'
Hbl
?
415ft
Ibl
2=1
lb
12
-
-
lls
󲰛
be
Ife
it
PREE
-0
by
convention
HD=IH7tfI→LTs
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Quantum Mechanics Homework: Spin States and Probability Calculations and more Assignments Quantum Mechanics in PDF only on Docsity!

Homework

IF 2

PnSlem#

= (^) ¥ It> - Es

I -

142 )^ =^ ¥ It)^ f^ Es I^ - 1437 = # It> - ea

l- s a) (^) Call the orthogonal,^ normalized vector 147 = (^) a ( t) t b (^) I (^) → Now require^ of 107--1 and < (^) 4147-- 54 , 14,7 -

  • Ca 'stl^ this - D # t) - EH
= a

Fs -^ b^

= (^) O a = 2b (^24) , 14,^

  • lat

Hbl?^ 415ft Ibl (^) 2= lb 12 -^ - lls be Ife it PREE

  • by convention HD=IH7tfI→LTs

2421427

Ca KH^ tbh)

(^) tails

)

= a

tb^

  • r÷ = o
a

= - b

if Ida =^ bird^ Its^ t^ b^ I (^) - 5/ = (^2) lbl 't lb't =^ I 612 = (^43) b -

  • E e

park E =^ - it

i.e -^ b^ -

  • (^) - Ig so that a =^ bird^ = FE (^) is real^ as (^) resumed ..- l4a7=flt7-I# Lol ,^1437 = Ca KH tb.FI#tt7-eIItD--aHuz
  • (^) b ' Iz (^) e i'b so a

=bae i

as e-^

' ¥ < 4314,

    • lb (^) 12+13/2--1 b- - free '

park G^

e THz (^) sothat^ a =^ posture, red

e. ' si:* c) <^ Hi^1457 and 24544C . ) <^4 , 1427 = 44214,7* , 1%7--44314, > & 4421437 -

  • 54314270

As

expected in general 54147--

IIM

Prudente 14,2=31+7+41- 1427 =^ It>^ tail

1437 =^3

It)^ - e

it 131 - y a) Normalize eachstate < (^4) , 14,^ = (^) (SCH (^) t 4th (31+7+41-7) = 32 t 42-- thus divide^ th)^ by TEs^ is l4i7=ZIt7t¥T < 421427 = 1 -^ 422-- t4z7=¥It7tZi## <43/437 =^9 t^ I^ = (^) to Hs7=f-¥eiM#

c) (^) Now find P (^) (t#

P (^) C-

x

) In this^ case^ we needto^ convert bro and (^) bet to^ be in the (^) same basis. Recall (^) It>^ × = (^) # It) t^ # I- I x

-^ - ¥ It ) - fat>

now written in S# basis^! Farah : P Ctx)^ = I (^) £+14,

ICE Alt fest) # (^) HAITI ÷:* :* . ÷ : For 42 :^ Phx) =^ I £+

    • (^) silt #← DC Its +^ E. HI = (^) 1¥ t (^) Fil '

= (^) Ciro (^) tf i) - Ei ) p To

    • ÷ : For 43 :^ P^ Ctx)^ = (^) I £+14,

4thHtt s

  1. Gro^ Its^ I

t Fa

I

    • (^) - CE -

I

-^ - Io t Io - Io Ce te I (^2) cos (E) =^ I = Io (^) (

9 t^

t - (^6) cos (^) ED pc :

"

" i

Far 45

Pay)^

If

= Io^ (

3 tie :#

3) (^3

  • (^) c. e- it"

Izo (^

gt ie "''

  • (^) sie
  • i^
  • (^) sine =^

Ii

Ce

ie

  • (^) e
    • ie

ice

it

  • e - it

) -^ -

2 sine

Io (^ 9+1 -^

(^6) sins

  • sin^

= BYZ

pc -

y%?n^

Ea

Prudently a) (^) Given (^) a thermal^ Chaudoin^ orientated^ inputstale, the first^ SG^ experiment should (^) splitthe^ atoms 50%- 50% (^) (modulo (^) statustrial fluctuations.) Thus there should be roughly 2x 29883 E^ -6701. atoms (^) exiting theoven.. The exact^ number^ can be^ calculated^ by Summy all (^) measured atoms. 29883 t^ 15070T 7473 t^7574 = 60k^. Hb>^

b) Has / , ←¥¥¥ i. Write (^) 14.7 (^). -^ I^4 a) in the (^) Sz basis (^). I (^4) a 7--1+7*145= (^) 1+ , = (^) Is (^) ( It> z ti (^) l- Y¥3ItI3;=ECHk-iH