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
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
