1 . I n tr o d u cti o n to th e co u r s e

1 . 1 W h y s t u d y Q u an t u m M e c h an i c s ?

1 . 2 S t r i k i n g C h ar ac t e r i s t i c s o f Q M

1 . 1 W h y s t u d y Q u a n t u m M e c h a n i c s ?

Q u a n t u m m e c h a n ic s ( Q M ) is a f u n d a m e n t a l a n d g e n e r a l t h e o r y t h a t a p p lie s o n a v e r y w id e r a n g e o f s c a le , f r o m s u b a t o m ic s y s t e m s t o a s t r o p h y s ic a l o b j e c t s .

It is n o w a d a y s a ls o a w id e ly a p p lie d s u b j e c t , w it h r e a l- lif e a p p lic a t io n s ( f r o m t r a n s is t o r s t o la s e r s ) a n d a n a c t iv e a r e a o f r e s e a r c h . F o r e x a m p le , it is a t t h e b a s is o f r e s e a r c h in n a n o t e c h n o lo g y , in m a t e r ia ls s c ie n c e , in s p in t r o n ic s ( w h e r e t h e e le c t r o n s p in r e p la c e s t h e c h a r g e a s t h e f u n d a m e n t a l u n it f o r s t o r in g in f o r m a t io n in a c o m p u t e r ) , e t c .

A ls o , t h e r e h a s b e e n a r e s u r g e n t in t e r e s t in t h e f u n d a m e n t a l t h e o r y o f Q M , d u e t o t h e in t e r e s t in q u a n t u m in f o r m a t io n a s w e ll a s t h e a v a ila b ilit y o f c o n t r o l o n s in g le q u a n t u m s y s t e m s 1 . A lt h o u g h y o u m ig h t n o t b e d ir e c t ly in t e r e s t e d in q u a n t u m in f o r m a t io n p e r s e , t h is d is c ip lin e h a s s h a p e d a n e w v ie w o f Q M t h a t is h a v in g im p a c t a ls o o n p r a c t ic a l a p p lic a t io n s . O n t h e p e d a g o g ic a l s id e , it h a s p u s h e d f o r a n e w w a y o f p r e s e n t in g Q M in c o lle g e c o u r s e s , t h a t I w ill t r y t o p a r t ia lly f o llo w h e r e , w it h m o r e e m p h a s is o n d is c r e t e s y s t e m s a n d a p p lic a t io n s in s t e a d o f a n h is t o r ic a l p r e s e n t a t io n o f Q M t h e o r y . ( Y o u p r o b a b ly a lr e a d y h a v e h a d t h a t k in d o f h is t o r ic a l in t r o d u c t io n , b o t h in u n d e r g r a d a n d in 2 2 .1 0 1 ) .

1 . 2 S t r i k i n g Ch a r a c t e r i s t i c s o f Q M

Q M is k n o w n f o r b e in g w e i r d , c o u n t e r in t u it iv e a n d d iffi c u lt t o u n d e r s t a n d 2 . T h e v a s t m a j o r it y o f p h y s ic is t s d o n o t w o r r y a b o u t t h e p u z z lin g a s p e c t s o f q u a n t u m m e c h a n ic s , b u t s im p ly u s e it a s a t o o l w it h o u t a s k in g q u e s t io n s o f p r in c ip le . N e v e r t h e le s s , t h e t h e o r e t ic a l a n d , e s p e c ia lly , e x p e r im e n t a l p r o g r e s s m a d e o v e r t h e p a s t t w e n t y y e a r s h a v e le d t o a b e t t e r g r a s p o f c e r t a in a s p e c t s o f t h e b e h a v io r o f q u a n t u m o b j e c t s .

In t h is c la s s w e w ill e x p lo r e t h e s e c o u n t e r in t u it iv e p h e n o m e n a , in p a r t ic u la r w e w ill e m p h a s iz e t h r e e c h a r a c t e r is t ic s o f Q M :

– D i s c r e te n e s s

T h is is t h e c h a r a c t e r is t ic t h a t g a v e t h e d is c ip lin e it s n a m e o f q u a n t u m m e c h a n ic s 3 . W h ile c la s s ic a l p h y s ic s a n d t h e w o r d a r o u n d u s s e e m s t o b e c o n t in u o u s , in Q M s o m e q u a n t it ie s c a n o n ly t a k e a d is c r e t e s e t o f v a lu e s . E x a m p le s a r e t h e d is c r e t e e n e r g y le v e ls o f a t o m s o r t h e a m o u n t o f e n e r g y e m it t e d in b la c k b o d y r a d ia t io n ( t h e s e a r e h i s t o r i c a l e x a m p le s ) . In t h e fi r s t p a r t o f t h e c o u r s e w e w ill f o c u s o n d is c r e t e s y s t e m s , in p a r t ic u la r o n a s y s t e m t h a t c a n a s s u m e o n ly t w o s t a t e s .

1 T h i s i s e x e m p l i fi e d b y t h e w o rk o f t h e t w o P h y s i c s N o b e l l a u r e a t e s i n 2 0 1 2 , D a v e W i n e l a n d a n d S e r g e H a r o c h e .

2 F o r t h o s e w h o a r e n o t s h o c k e d w h e n t h e y fi r s t c o m e a c r o s s q u a n t u m t h e o r y c a n n o t p o s s i b l y h a v e u n d e r s t o o d i t . N i e l s B o h r , q u o t e d i n H e i s e n b e r g , W e r n e r ( 1 9 7 1 ) . P h y s i c s a n d B e y o n d . N e w Y o r k : H a r p e r a n d R o w . p p . 2 0 6 . I t h i n k I c a n s a f e l y s a y t h a t n o b o d y u n d e r s t a n d s q u a n t u m m e c h a n i c s . R i c h a r d F e y n ma n , i n T h e C h a r a c t e r o f P h y s i c a l La w ( 1 9 6 5 )

3 E t y mo l o g y : La t i n , n e u t e r o f q u a n t u s h o w m u c h . P l u r a l q u a n t a . 1 a : q u a n t i t y , a m o u n t . b : a c e r t a i n o r a n a l l o t t e d a mo u n t

: p o r t i o n ( f r o m M e r r i a m - W e b s t e r d i c t i o n a ry ) .

7

– In te r f e r e n c e

In t e r f e r e n c e a n d d iff r a c t io n a r e c h a r a c t e r is t ic s o f w a v e s , in p a r t ic u la r lig h t . In Q M it w a s f o u n d t h a t in t e r f e r e n c e a ls o a p p lie d t o m a t t e r a n d it is a c t u a lly a g e n e r a l p h e n o m e n o n . E .g . d iff r a c t io n o b s e r v e d w it h la r g e o b j e c t s s u c h a s f u llu r e n e s ( C 6 0 ) . W e w ill s e e h o w in t e r f e r e n c e is lin k e d t o t h e p o s s ib ilit y o f fi n d in g a s y s t e m in a s u p e r p o s it io n s t a t e a n d f u r t h e r e x p lo r e e v e n w e i r d e r p h e n o m e n a s u c h a s e n t a n g le m e n t .

– Ph a s e c o h e r e n c e

T h e a b ilit y t o o b s e r v e in t e r f e r e n c e s is lin k e d t o a b ilit y f o r a s y s t e m t o m a in t a in a p h a s e c o h e r e n c e a m o n g t h e d iff e r e n t p a r t s in a s u p e r p o s it io n s t a t e . C o n v e r s e ly , t h e lo s s o f t h is p h a s e c o h e r e n c e is lin k e d t o t h e d is a p p e a r a n c e o f t h e Q M p r o p e r t ie s o f a s y s t e m a n d t h e o b s e r v a t io n o f c la s s ic a l p h y s ic s b e h a v io r . T h is o c c u r s e .g . w h e n t h e s y s t e m in t e r a c t s w it h a n e n v ir o n m e n t a n d a g o o d p a r t o f t h is c o u r s e w ill f o c u s o n t h e s t u d y o f t h e s e s o - c a lle d o p e n q u a n t u m s y s t e m s .

R e f e r e n c e s

A . T o n o m u r a , J . E n d o , T . M a t s u d a , T . K a w a s a k i a n d H . E z a w a , D e m o n s t r a t i o n o f s i n g l e - e l e c t r o n b u i l d u p o f a n i n t e r f e r e n c e p a t t e r n A m e r ic a n J o u r n a l o f P h y s ic s 5 7 , 2 1 1 7 - 1 2 0 ( 1 9 8 9 )

O nl i ne V i de o

M . S . C h a p m a n , T . D . H a m m o n d , A . L e n e f , J . S c h m ie d m a y e r , R . A . R u b e n s t e in , E . S m it h , a n d D . E . P r it c h a r d ,

P h o t o n S c a t t e r i n g f r o m A t o m s i n a n A t o m In t e r f e r o m e t e r : C o h e r e n c e L o s t a n d R e g a i n e d P h y s . R e v . L e t t . 7 5 , 3 7 8 3 - 3 7 8 7 ( 1 9 9 5 )

• M . A r n d t , K . H o r n b e r g e r , A . Z e ilin g e r P r o b i n g t h e l i m i t s o f t h e q u a n t u m w o r l d P h y s ic s W o r ld 3 5 - 4 0 ( M a r c h 2 0 0 5 )

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22.51 Quantum Theory of Radiation Interactions

Fall 201 2

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