is completely general whenever you have waves from two sources interfering. 2

Size: px

Start display at page:

Download "is completely general whenever you have waves from two sources interfering. 2"

Scarlett Crawford
6 years ago
Views:

1 MAKNG SENSE OF THE EQUATON SHEET terferece & Diffrctio NTERFERENCE r1 r d si. Equtio for pth legth differece. r1 r is completely geerl. Use si oly whe the two sources re fr wy from the observtio poit. is completely geerl wheever you hve wves from two sources iterferig. d si d d y pplies to iterferece from multiple slits. is the phse differece betwee L wves from successive slits t the poit of observtio. d is the slit seprtio. is the wvelegth. is the positio o the scree mesured s gle. y is the positio o the scree mesured s distce. L is the distce from the slits to the scree. si pplies to iterferece from multiple slits. is the gulr positio of the th order pek. Note d tht: si for smll gles d tht where is the gulr seprtio betwee d d successive peks. 41 cos pplies oly to the superpositio of wves. DFFRACTON si pplies to diffrctio. is the pth legth differece betwee the top d bottom of the slit of width.... pplies to diffrctio. Here is the phse differece betwee the wves comig from the top d the bottom of the slit. m si pplies to diffrctio. is the gulr positio of the m th order miimum cused by diffrctio.

2 NTERFERENCE PLUS DFFRACTON 1 si / / gives the shpe of the diffrctio ptter (the evelope). N si N / si / 1 gives the shpe of the iterferece ptter (the peks). N is the umber of slits. Note tht: N / si / si / si / gives the totl itesity ptter. RESOLUTON OF LENSES, GRATNGS, ETC is the miimum gulr seprtio of two objects resolvble through 1D slit of width. 1. is the miimum gulr seprtio of two objects resolvble through les or circulr perture of D dimeter D. c c lso be tke to me the miimum resolvble gle. mi 1 pplies to resolutio of two iterferece peks through diffrctio grtig. is the miimum Nm resolvble wvelegth differece. N is the umber of slits. m is the order of the pek.

3 MAKNG SENSE OF THE EQUATON SHEET Qutum Physics, Prt ENERGY & MOMENTUM mx stop KE ev hf h f f pplies to the photoelectric effect. The mximum kietic electros comig off the metl is KE mx. V stop is the stoppig voltge. hf is the eergy of the photo. is the work fuctio of the metl. Note: Multiplyig y voltge V by electric chrge e gives eergy i ev umericlly equl to the voltge. For exmple: V ev e f 69 volts, the 69 volts 69 ev. KE 1 p m mv gives the kietic eergy for y mssive prticle. Note tht photo is ot mssive prticle. hc 14eV m E pc hf gives the eergy of photo. For wvelegth. 14eV m use ometers for h/ p pplies to both mssive prticles d photos. p h KE m m gives the kietic eergy of y mssive prticle. 1.55eV m KE is for electros. SCHRODNGERS EQUATON U x i m x t x d t. is the time depedet schrodiger equtio. Here cpitl psi is fuctio of i t x, t x e is the time depedet solutio to the schrodiger equtio. Lowercse psi x is solutio to the time idepedet schrodiger equtio. U x E is the time idepedet schrodiger equtio. E is the eergy of the prticle. m x x x x * is the probbility desity fuctio, it gives the probbility per uit legth tht the prticle c be foud t x. The * deotes complex cojugte.

4 b b P x dx gives the probbility tht the prticle c be foud betwee x= d x=b. ikx t x, t Ae is the solutio to the schrodiger equtio for free prticle (the potetil eergy U(x) is ero). k Note tht E, the eergy of the prticle. m xp is the Heiseberg ucertity priciple. The ucertity i mometum multiplied by the ucertity i positio must be greter th or equl to. x si x L L gives the th stte wvefuctio for prticle i ifiite squre well of legth L. h E E m L 8mL 1 gives the th stte eergy for prticle i ifiite squre well of legth L. L gives the th stte wvelegth of the wvefuctio for prticle i ifiite squre well of legth L.

5 MAKNG SENSE OF THE EQUATON SHEET Qutum Physics, Prt THE FNAL STUFF T e where KL m K U E o T is the probbility tht prticle of eergy E c tuel through potetil eergy brrier of legth L d height U. t E h E 1 This equtio gives the hlf-period of the time-depedet wvefuctio tht results from superpositio of two sttiory sttes. e Ur r The coulomb potetil, or i other words, the potetil tht electro i hydroge tom feels. e is the electric chrge (d here we ssume there is sigle proto; otherwise it would be e(ze)). r is the distce to the ucleus. 1/ 4 is costt ,, x y si x si y si bc b c This is the wvefuctio for prticle i 3-dimesiol ifiite squre well of legths, b, c, i the x, y, directios respectively. 1,, d 3 re idepedet of ech other, but must be >1. h 1 3 E,, 1 3 8m b c Allowed eergies for the prticle i 3D ifiite squre well. 1 r e 1s 3 r/,, The groud stte wvefuctio for the electro i the hydroge tom. is the bohr rdius. E 13.6 ev : Eergy levels for the hydroge tom.

6 Z E 13.6 ev Eergy levels for electro subject to Z positive chrges. Note tht Z=1 gives the hydroge equtio. 4 P r dr r r dr You probbly wo t hve to use this equtio. Wht it mes it tht is equl to Pr probbility per uit of rdil distce 4r r. To fid probbility over whole rge of r, itegrte with respect to r. r,, R r Y, lm l lm Geerl form of hydroge wvefuctios. R is the rdil wvefuctio d Y is the sphericl hrmoic. They re idepedet of ech other. L l l 1 Very importt. L is totl gulr mometum. l is the fmilir qutum umber. L m Also importt. Agulr mometum i directio is proportiol to m qutum umber. Y, Y, Y = The sphericl hrmoics for l = d l =1. U B Potetil eergy of prticle i mgetic field is equl to mgetic momet times field stregth. F db : Follows directly from bove. Tke derivte w.r.t. e m e d S i the directio. Mgetic momet of electro. e is electric chrge. m e is mss. S is the spi of the electro 1 E : eergy levels of the hrmoic oscilltor. S S s s 1 : S is the spi gulr mometum. s is the spi qutum umber. ms : S is the compoet of the spi gulr mometum. m s is other qutum umber relted to spi s, just like m l reltes to l.

Lecture 38 (Trapped Particles) Physics Spring 2018 Douglas Fields

Lecture 38 (Trapped Particles) Physics Spring 2018 Douglas Fields Lecture 38 (Trpped Prticles) Physics 6-01 Sprig 018 Dougls Fields Free Prticle Solutio Schrödiger s Wve Equtio i 1D If motio is restricted to oe-dimesio, the del opertor just becomes the prtil derivtive