(1892-1987,French)

NewCh6 (Old Ch7) biosfigstabs biosfigstabs 6.1
Chapter 6 Biographies, Figures, and Tables
Biographies
LOUIS DE BROGLIE (1892-1987, French). The son of a noble French family, de Broglie graduated
from the Sorbonne in history. He became interested in physics during World War I, and his idea that
all particles have an associated wave was in his PhD thesis in 1924. This proposal, which earned him the 1929 Nobel Prize, was an essential link between the Bohr model and modern quantum mechanics.
MAX BORN (1882-1970, German-British). Born is best known for his work on the mathematical structure of quantum mechanics and the interpretation of the wave function. When Hitler came to power, Born left Germany and became a professor at Edinburgh University. He won the Nobel Prize in 1954 for his contributions to quantum theory.
NewCh6 (Old Ch7) biosfigstabs biosfigstabs 6.2
WERNER HEISENBERG (1901 -1976, German). After
earning his PhD at Munich, Heisenberg worked with Born and then Bohr. His many contributions to modern physics include an early formulation of quantum mechanics in terms of matrices, several ideas in nuclear physics, and the famous uncertainty principle, for which he won the 1932 Nobel Prize. He remained in Germany during World War II and worked on nuclear reactor design. The possibility that he might be working on an atomic bomb for the Nazis so frightened the Allies that a plan was devised to have him assassinated. An American agent, named Moe Berg, posed as a physicist and met with Heisenberg when he was visiting neutral Switzerland in late 1944. After talking with Heisenberg, Agent Berg decided that the Germans had made little progress toward a bomb and chose not to kill him. JOSEPH FOURIER (1768-1830, French) As a young man, Fourier couldn't decide whether to devote his life to mathematics, the priesthood, or politics. He finally became a politically active mathematician. Acting as scientific advisor, Fourier accompanied Napoleon's army to Egypt in 1798, where he carried out archeological expeditions and established educational institutions. He was a prolific and well-respected mathematician; his most famous work wasOn the Propagation of Heat in Solid Bodies, written in 1807. In this book, he developed the technique now called Fourier analysis and applied it to problems of heat flow. The work was controversial. Many eminent mathmeticians of the time refused to believe that functions with discontinuities could be written as sums of smoothly varying sine and cosines.
NewCh6 (Old Ch7) biosfigstabs biosfigstabs 6.3
Figures
FIGURE 6.1 If an electron wave is pictured as circling around the atomic nucleus, its wavelength
must fit an integer number of times into the circumference.
FIGURE 6. 2 The electron tube in which Davisson and Germer observed the diffraction of electron waves. Notice the graduated turntable for rotating the target crystal near the center of the tube. (Courtesy AT&T Archives.)
FIGURE 6. 3 Diffraction rings produced by diffraction of waves in polycrystalline metal samples with
(a) X rays, (b) electrons, (c) neutrons. (Courtesy Educational Development Center and Prof. C. G. Shull.)
FIGURE 6. 4 Two-slit interference patterns produced by light and electrons. (Courtesy Addison-Wesley and Prof. C. J?nsson.)
FIGURE 6. 5 Schematic diagram of the two-slit experiment. The graph shows the intensity as a function of position along the film.
FIGURE 6. 6 Development of a two-slit interference pattern. The three pictures show the pattern after
2
40, 200, and 2000 electrons (or photons) have arrived. The graph shows the intensity of the wave as a function of position. Note that each particle arrives at a definite position, but more particles arrive
where 2
is larger.
FIGURE 6. 7 To find out which slit the electron passes through, we shine a narrow beam of light through one of the slits.
FIGURE 6.8 Five successive snapshots of the sinusoidal wave (6.18). Any definite point on the wave, like the crest on which the surfer is riding, moves steadily to the right. At any fixed positionx, the string bobs up and down sinusoidally in time.
+ x
FIGURE 6.9 A localized wave packet, which is nonzero in an interval x and zero elsewhere±. A particle with this wavefunction would not be found outside the interval x.±
y
a
x
FIGURE 6.10 A simple period function, a series of square pulses with widtha with period.
(a)
(b)
(c)
(d)
FIGURE 6.11 The Fourier sum version of the periodic function in Fig.6.10. (a) The fundamental term only. (b) The sum of the first 3 sinusoidal terms, (c) the first 8 terms, (d) the first 30 terms.
y
a k = 2 /
x k
k
k
FIGURE 6.12 A periodic function with period becomes anon-periodic function in the limit that. As the period grows, the spacing ofk's in the Fourier sum goes to zero.
FIGURE 6.13 A wavepacket (below) is made up of a series of sinusoidal waves of various wavelengths (above) .
f(x)A(k)
2 k
2 x
FIGURE 6.14 A narrow wavepacket (small x) corresponds to a large spread of wavelengths (largek).
A wide wavepacket (large x) corresponds to a small spread of wavelengths (smallk).
y
2
2N~ /2
~
x N cycles
FIGURE 6.15 Two cosine functions with wavelengths differing by 2..
FIGURE 6.16 The Heisenberg microscope(a). minimum experimental uncertainty in the particle's position x is determined by the microscope's resolution as x l min l /d. (b) The direction of a photon entering the microscope is uncertain by an angle of order/l, therefore, the photon gives the
particle a momentum (in the x direction) which is uncertain by p x p ph d/l/
FIGURE 6.17 Six successive views of a wave packet, or group, moving to the right. The velocity of the whole packet is v pack often called the group velocity. The velocity of an individual crest, like the one carrying the surfer, is v wave, the wave velocity (or phase velocity). For this v wave > v pack , and the surfer moves steadily toward the front of the packet. The two sloping dotted lines indicate the motion of the front and back of the packet; the sloping dashed line indicates the motion of a single wave crest.
FIGURE 6. 18 (a) If two waves with slightly different frequencies 1 and 2 are superposed, they are alternately in and out of step.(b) The resultant wave shows the phenomenon of beats, in which a wave of frequency( 1 2 ) / 2 is modulated by an envelope, which oscillates at the difference frequency.
FIGURE 6.19 = Old 7.21 (Problem 6.XX = Old 7.28)
FIGURE 6.20 = Old 7.22 (Problem 6.XX = Old 7.29)
NewCh6 (Old Ch7) biosfigstabs biosfigstabs 6.11 FIGURE 6.21 = new (Problem 6.XX = Old 7.29)
FIGURE 6.22 = Old 7.23 (Problems 6.XX = Old 7.31, 7.32, and 7.34)
04/05/13 4:01 PM。