**12 ** 量子物理

**Sections**

**1.Photon and Matter Waves**
**2.Compton Effect**

**3.Light as a Probability Wave**
**4.Electrons and Matter **

**Waves**

**5.Schrodinger’s Equation**
**6.Waves on Strings and **

**Matter Waves**

**7.Trapping an Electron**
**8.Three Electron Traps**
**9.The Hydrogen Atom**

**12-1.1 Photon and **

**Matter Waves (** 光子 **和物質波 )**

• **Light Waves and **
**Photons**

s J 10

63 .

6

) energy photon

(

34

*h*

*hf*
*E*

*f*
*c*

**The Photoelectric Effect**

•

**First Experiment**

**(adjusting V)– **

** the stopping potential **
**V**_{stop}

• **Second Experiment **
**(adjusting f)– **

** the cutoff frequency f**_{0}

stop

max

*eV*

*K*

**The experiment**

光電子的最大動能與 光強度無關

低於截止頻率時即使光再 強也不會有光電效應

**The plot of V**

_{stop}**against f**

**The Photoelectric ** **Equation**

s J 10

6 . 6

) (

34 stop

max

*h*

*f* *e*
*e*

*V* *h*

*K*

*hf* **Work **

**functio**
**n**

**12-1.2** ^{ Compton }

^{ Compton }

**Effect**

### momentum) (photon

### *h* *c*

*p* *hf*

康普 吞效 應實 驗圖 表

康普吞效應圖示

*mv*
*p*

*h*
*p*

*h* *mc*
*h*

*mc*
*f*

*h*
*hf*

*mc*
*K*

*K*
*f*

*h*
*hf*

*e*

*X*

/

) 1 (

) 1 (

) 1 (

2

2

**Energy and momentum **

**conservation**

) cos

1 (

sin sin

0

cos cos

*mc*
*h*
*h* *mv*

*h* *mv*
*h*

**Frequency shift**

**Compton **
**wavelength**

**12-1.3 Light as a ** **Probability Wave**

**The **

**standard **
**version**

** The single-photon, **

**double-slit experiment is **
**a phenomenon which is **
**impossible, absolutely **
**impossible to explain in **
**any classical way, and **

**which has in it the heart **
**of quantum mechanics - **
**Richard Feynman**

**The Single-Photon ** **Version**

**First by Taylor in 1909**

**The Single-Photon, **

**Wide-Angle Version **

**(1992)**

**Light is generated in the **
**source as photons**

**Light is absorbed in the **
**detector as photons **

**Light travels between **

**source and detector as a **
**probability wave**

**The postulate**

**12-1.4 Electrons and ** ** Matter Waves**

*p*

*h*

• **The de Broglie wave length**

###

• **Experimental verification in **
**1927**

• **Iodine molecule beam in **
**1994 **

**1989 double-slit ** **experiment**

**7,100,3000, 20,000 and 70,000 **
**electrons**

**Experimental ** **Verifications**

**X-**
**ray**

**Electr**
**on **
**beam**

苯環 的中 子繞 射

**12-1.5 Schrodinger’s ** ** Equation**

• **Matter waves and the wave **
**function**

• **The probability (per unit **
**time) is **

*t*

*e*

*i*

*z* *y* *x*

*t* *z* *y*

*x* , , , ) ( , , )

### (

^{}

^{}

###

###

###

###

^{2}

### ie. *

**Complex **
**conjugate**

共軛複數

**The Schrodinger **

**Equation from A Simple ** **Wave Function**

*m* *k*

*m* *p*

*E*

*k* *h*

*p*

*kx* *B*

*kx* *A*

*e* *z*

*y* *x*

*t* *z* *y*

*x*

^{i}

^{t}### 2 / 2

### / /

### ) cos(

### ) sin(

### ) ,

### , (

### ) ,

### , ,

### (

2 2

2

###

###

###

###

###

###

###

###

###

###

^{}

###

###

###

^{}

*dx* *E*
*d*
*m*

*dx*
*d*
*E* *m*

*dx*
*k* *d*

*k*
*dx*

*d*

*kx*
*B*

*kx*
*A*

2 2 2

2 2 2

2 2 2

2 2

2

2

2 1

1 /

) cos(

) sin(

**1D Time-independent **

**SE**

*i* *t*
*m* *V*

*i* *t*
*m*

*dz* *E*
*d*
*dy*

*d*
*dx*

*d*
*m*

*dx* *E*
*d*
*m*

2 2

2 2

2 2 2

2 2

2 2

2 2 2

2 2

) 2 (

2

**3D Time-dependent SE**

**12-1.6** ** Waves on **

**Strings and Matter **

**Waves**

**Confinement of a Wave **
**leads to Quantization – **

**discrete states and discrete **
**energies**

## 駐波與量子化

**Quantization**

*n* *=* *,* *,* *,*

*L*
*n* *v*

*f* *v*
*n*

*L* 0 1 2

2

= 2

駐波：

number

quantum :

, 3 , 2 , 1

, ) sin(

, 3 , 2 , 1 2

*n*

*n*
*L* *x*

*A* *n*
*y*

*n* *n*
*L*

*n*

**12-1.7 Trapping an ** **Electron**

**For a string** ：

, 3 , 2 , 1

, 8

/

2 / ,

2 /

/

2 2

2

*n*
*mL*

*h*
*n*
*E*

*n*
*L*

*mE*
*h*

*p*
*h*

*n*

**Finding the Quantized **

**Energies of an infinitely **

**deep potential energy well**

**The ground **
**state and **

**excited **
**states**

**The Zero-**
**Point **

**Energy **

** n can’t be 0**

**The Energy Levels **

能階
###

###

###

### , 3 , 2 , 1

### , ) (

### sin

### , 3 , 2 , 1

### , ) sin(

### , 3 , 2 , 1

### , ) sin(

2 2

2

###

###

###

###

###

*n* *L* *x*

*A* *n*

*n* *L* *x*

*A* *n*

*n* *L* *x*

*A* *n* *y*

*n*
*n*
*n*

###

###

###

**The Wave Function ** **and Probability **

**Density**

_{For a }**string**

**The Probability **

**Density**

### • **Normalization (**

歸一
**化 )**

##

^{}

###

_{n}^{2}

### ( *x* ) *dx* 1

**Correspondence ** **principle **

**(**

**對應原理 )**

**At large enough quantum **

**numbers, the predictions of **
**quantum mechanics merge **
**smoothly with those of **

**classical physics**

0 )]

( 8 [

2 2 2

2

###

###

###

*x*
*E*

*h* *E*

*m*
*dx*

*d*

*pot*

**A Finite Well **

有限位能井
**The probability **

**densities and energy **

**levels**

**Barrier Tunneling**

穿隧效應
**STM **

掃描式穿隧顯微鏡
**Piezoelectricity**
**of quartz**

**12-1.8 Three Electron ** **Traps**

• Nanocrystallites 硒化鎘奈米 那種顏色的顆粒比較小晶粒

*t*
*t*

*t* *E*

*ch*
*c **f*

2 2 2

*8mL*
*h*
*E** _{n}*

*n*

**A Quantum Dot **

**An Artificial Atom**

**The number of electrons can be controlled**

**Quantum Corral**

## 量子圍欄

**12-1.9 The Hydrogen ** **Atom**

### • **The Energies**

### , 3

### , 2 , 1

### ev , 6

### . 13 1

### 8

### 4 1 4

### 1

2 2

2 2

0 4

2

0 2

1 0

###

###

###

###

###

###

###

###

*n* *n* *n*

*h* *E* *me*

*r* *e* *r*

*q* *U* *q*

*n*

###

###

###

氫原 子能 階與 光譜 線

**Bohr’s Theory of **

**the Hydrogen Atom**

### radius) (Bohr

### pm 29

### . 5 ) 1

### (

2 0 2

/ 2

/ 3

###

###

###

^{}

*me* *a* *h*

*a* *e*

*r*

^{r}

^{a}###

###

###

**The Ground State Wave **

**Function**

**Quantum Numbers ** **for the Hydrogen **

**Atom**

**The Ground State Dot **

**Plot**

## 氫原子的量子數

**N=2, l=0, m**

_{l}