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Class notes PHY-20006 Quantum Mechanics £20.48
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Class notes PHY-20006 Quantum Mechanics

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This is a good set of notes introducing students to the basic concepts of quantum mechanics without delving into the complex reasonings behind why things happen as they do. We start off with time independence and the schrödinger equation, parity and the infinite square well all the way to the 3D...

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  • February 22, 2025
  • 86
  • 2023/2024
  • Lecture notes
  • Dr pierre maxted
  • All classes

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Lec 1 : Quantum vs Classical MoRs



Classical
Physics : Quantum :

o
ramlike



duality
ou




Bodies w/ defined position and momentum
wave-particle
·
·




·

motion described
by Newton's laws of motion
uncertainty =
DcDp
-
=
E (physical inherent property)
Concertainty fignorance)
Maxwell's
equations describe EM waves
Spatrick's handbook
·




quantization of =>
Elevels for bound
·




energy
systems eges in atems




Zero-pointE E min E for
physical system) O
·




Formalism : how to do QM
⑪including vasuum
eg virtualPas

#terpellation : What QM means
X




When to use QM :


·




required for systems with sizedinplacks

, e
g
.
de
Broglie wavelength for atoms in N2


·
X =
t ,
what is
p
!



·




Evib EKT =
, K = 1835K"
T = Book
h = 7x18345s


KE =
Ep 10 kgm =




.. 4 ~0 7nm
.




Assize : -O Inm .




7-physical size

=>
quantum effects are
strong


Time-dependent Seg s
E

↓
Id time
↓



S
time-independent
in 1-dimension


↓
1 Ewell QHo
, etc)


↳
,

, I


3a
, y(f ,
t)
Hatom
Two-particle (P(F ,
=2 , ..., t)]
SchrödingeEgt
(time-dependent)
:

ihonian"/ "E
operator
>
-
mathematiadescription et
o




contains all observable information for
I
function"
et

"War
: =
sye
a




=>
complex function (not related to real
physical systems.
of + time
space

e .




g
Id particle :




E ((x t)
=

,
= a( t) ,
+ ib( ,
t) y in this form )

3d particle :




I =
[(x y t) , ,
z
,
=
[(f t) ,




·




particle in
villy abstract space


for particles spin (s)
·


2 in 3d with :




I =
E( ,
m 2 ,2
,
,
t)
S




·


# =
"do this to function" ? >
-
Set of instructions/mathematical recipe to extract information from 4 abt total E

, ·


TDSE determines how wit's evolve in
given potential => QM
equivalent of Newton's 249 Law of mot



Conditions that
Schrodinger equation satisfies
1) wave
eqt that
gives solutions wh X =
t
2) energy
of solution => E = hr


3) non-relativistic case : E= V >
- V =
potential

4) equation is
LIVEAR => E.. E2 solutions


=> C
, I, 22 also are solutions

=>
constructive/destructive interference of waves




5) no Facts on
particle w/V constant => momentum constant

=> wave solk has constant (de Broglie) wavelength

Schrodinger eqt only gives predictions => consistent w/ experiments
·




phenomena it describes # understood basis of classical
physics
·



on




·

no REAL functions satisfy these conditions for reasonable wave
equation
any
=> no choice abt complex functions to describe behaviour of
quantum systems

·




valid solt's >
Wave functions

·




interpretation of QM = nature of wif's and their connection to reality
#
agreed

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