Lecture physics a2 quantum mechanics

QUANTUM MECHANICS Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016 VOCABULARY • Wave Particle Duality • Uncertainty • Heisenberg’s Uncertainty Principle • Wave Matter • De Broglie’s wavel[.]

QUANTUM MECHANICS

Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016

VOCABULARY

• Wave - Particle Duality

• Uncertainty

• Heisenberg’s Uncertainty Principle

• Wave Matter

• De Broglie’s wavelength

CONTENTS

• Wave – Particle Duality of Matter

• De Broglie’s Hypothesis – Matter wave

• Diffraction of electron wave by single slit

• Heisenberg’s Uncertainty Principle

particular, of the happenings on an atomic scale

Things on a very small scale behave like nothing that you have any direct experience about They do not

behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or

weights on springs, or like anything that you have ever seen.”

Richard P Feynman

Ni Crystal

detector

q

 In 1927-8, it was shown

(Davisson-Germer) that, like x-rays, ELECTRONS

can also diffract off crystals !

q

Interference peak !

Electrons can act like waves!!

What does this mean?

In discussion section:

q

 DeBroglie (1924) proposed that, like

photons, particles have a wavelength:

l = h/p Inversely proportional to

momentum

• We will see later that the discrete

atomic emission lines also arise from

the wavelike properties of the

electrons in the field of the nucleus:

Atomic

hydrogen

“Double-slit” Experiment for Electrons

 Electrons are accelerated to

50 keV  l = 0.0055 nm

 Central wire is positively

charged  bends electron

paths so they overlap

 A position-sensitive detector

records where they appear

 << 1 electron in system at

any time

[A TONOMURA (Hitachi) pioneered electron holography]

LIGHT has nature of Wave–Particle Duality

• Wave: Electromagnetic Wave : Interference, Diffraction

- Particle: PHOTON: Photoelectric effect, Compton Effect

k p

k

2

h p

: momentum photon

2 h

E :

energy photon







 l



 l















vector unit

:

n

n

2 k

: vector wave

2 vT

2 v

k

: number wave







l



 l













Electromagnetic Wave:

Consider a light plane wave,

propagating in the z direction:

Wave function at point O: o = A cos (t)

Wave function at point M: (M, t)=A cos ((t-z/v)) =Acos(t-kz)

:

M (x,y,z)

z

r



z

k 

) r k t

cos(

A )

t , M









 















function

ve complex wa of

part real function

wave real

) k -t i(

) k -t i(

-t) (M, Ψ Re

t) Ψ(M, :

convention the

with

function wave

complex Ae

t)

(M,

Ψ

Ae t)

(M,

Ψ

: n descriptio complex

in



















vector unit

: n

n

2 k

: vector wave

2 vT

2 v

k

: number wave







l



 l













de Broglie’s hypothesis 1924

Light is dualistic in nature, behaving in some situations like waves and in others like particles If nature is symmetric, this duality should also hold for matter Electrons and protons, which we usually think of as particles, may in some situations behave like waves

k p

;

h p

h

E





 l











If a particle acts like a wave, it should have a wavelength and a frequency

De Broglie postulated that a free particle moving with speed v, having kinetic

energy E, momentum p should have a wavelength l , frequency  related to its momentum p and its energy E by: