introduction to quantum mechanics

... “third” to “last”; next lines, change to read “ whereas the middle two occur three ways ” • page 205, last paragraph: change every 10 to 13 (eight times); in line change “the second” to “either ... x to y; add “is”: “ and is polarized ” • page 322, Prob 9.20 (b): change “w” to “ω” in the last line • page 323, lines and 3: change “I” to “you” (twice) • page 330, line 5: change “it” to ... page 353, Fig 11.2: change “a” to “α” (three times) • page 359, Table 11.1: change every z to x (18 times) • page 363, second equation from the bottom: change δ to δ • page 365, Fig 11.7: remove...

phillips a.c. introduction to quantum mechanics

... Edition A C Phillips Computing for Scientists: R J Barlow and A R Barnett Nuclear Physics: J S Lilley Introduction to Quantum Mechanics: A C Phillips INTRODUCTION TO QUANTUM MECHANICS A C Phillips ... the word same: If the photon moving to the East, say, is observed to have right-hand circular polarization, then the photon moving to the West is certain to be found to have right-hand circular ... circular polarization But if the photon moving to the East is observed to have left-hand circular polarization, then the photon moving to the West is certain to be found to have left-hand circular polarization...

introduction to quantum mechanics

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Introduction to fluid mechanics - P1

... beginning of fluid mechanics Fig 1.3 Ancient Greek ship depicted on old vase inclination or supply pressure had to be adjusted to overcome friction with the wall of the conduit This gave rise to much ... was the first to find the least resistive ‘streamline’ shape 4 History of fluid mechanics Leonardo da Vinci (145 2-1 519 ) An all-round genius born in Italy His unceasing zeal for the truth and ... origin of the ship is not clear, but it is easy to imagine the course of progress from log to raft, from manual propulsion to sails, and from river to ocean navigation The Phoenicians and Egyptians...

Introduction to fluid mechanics - P2

... Kinematic viscosity B Y units 0 1 0 0 m kg -3 -1 1 1 -1 -1 -2 -2 -2 -2 -1 -1 S mls m/s2 kg I m3 N = kg m/s2 Pa = N/m2 J Pa s m2/s Characteristics of a fluid 2.2.2 Dimension All physical quantities ... proportional to the velocity gradient duldy Such fluids are called Newtonian fluids On the other hand, liquid which is not subject to Newton's law of viscosity, such as a liquid pulp, a high-molecular-weight ... only too well known There are so many scientific terms named after Newton (Newton's rings and Newton's law of motion/ viscosity/resistance) that he can be regarded as the greatest contributor to...

Introduction to fluid mechanics - P3

... semiconductor strain gauge PGM-C Pressure range (MPa) Natural frequency (kHz1 Response frequency (kHz1 PE-J, P (a) Small size 0. 2-1 o 2 5-4 0 5-8 (b) For indicating pressure of an engine 5-2 0 2 5-4 0 5-8 ... pdAor ( ) p+-dz dA-pgdAdz=O 24 Fluid statics Fig 3.4 Balance of vertical minute cylinder dp _ - -PS &" (3.6) Since p is constant for liquid, the following equation ensues: p = -pg J dz = -pgz+C (3.7) ... measuring fluid is used Fig 3.8 Differential manometer (2) 28 Fluid statics Fig 3.9 Inclined manometer Thus PI - P2 = (P‘ - P)SH’ (3.21) and in the case where p is a gas, PI - P2 = P’SH’ (3.22) A U-tube...

Introduction to fluid mechanics - P4

... direction moves to A‘B’ while rotating by dq, and AD in the y direction rotates by de, Thus av de - - dxdt - ax at4 d = dydt E aY de - L = - d av d~ t I - dx ax de = dt dE2 dy au - ay The angular ... case of two-dimensional flow where w = V is an operator which represents a a a ax ay az i-+j-+k- where i,j , k are unit vectors on the x, y z axes 50 Fundamentals of flow Fig 4.11 Tornado movement ... dA), to obtain dr=udx+ ( 3( v+-dx dy- u+-dy dx-vdy= ( g - g ) d x d y = [dxdy = CdA (4.10) C is two times the angular velocity w of a rotational flow (eqn (4.6)), and the circulation is equal to...

Introduction to fluid mechanics - P5

... momentum: - (D’ increase in momentum: R - d2)pu: 71 -p[D2u: 71 + -d’pui - (0’ - d2)u: - d’ui] 71 force acting on the fluid: -D’(p, - p ) By the law of momentum, ~ [ D ’ u - (D’ - d2)u: - d ’ ~ ... respectively Then from Bernoulli’s equation Pl u: 2g P2 -+ -+ z PS VI - PS 29 +-+ z2 Assuming that the pipe line is horizontal, z1 = 22 v2 - v: - - PI - P2 - 29 P9 From the continuity equation, 01 = V2A2IAl ... level falling by -dH (Fig 5.12) Then dQ = C a m d t = -dHA -AdH dt = c a m 1:: A dt = - H2dH z EdH, The time needed for the water level to descend from HI to H2 is 2A t241 =-( fi-fi) c a a (5.26)...

Introduction to fluid mechanics - P6

... following equation: a u a u au du = -dt + dx -dy at ax ay + Therefore, du _ - -au + -audx- ~ -audy- + ~ -+ +u dt at axdt aydt at au ax aU ay Substituting this into eqn (6.4), Next, the force F acting ... d y = -h3 dP 12pdx From this equation, the mean velocity u is Q = - = -h2 dP = - u1 h 12pdx 1.5 (6.23) (6.24) The shearing stress z due to viscosity becomes ldp z = p - du - - - ( h - ~ ) =dy ... = t U / l = av*/ax *- &*lay* Re = p U l / p (6.17) e* Using these equations rewrite eqn (6.16) to obtain the following equation: ai* - * ay* a[* ax* ay* -+ v *-= - aC Re (ax*’ -+ - ) : (6.18) Equation...

Introduction to fluid mechanics - P7

... efficiency q for a diffuser is therefore P2-P1 - q=-P2th - PI hs (0: - U:)/2s (7.31) Substituting in eqn (7.28), the above equation becomes q = - c - 02 - - + 02 - Al/A2 + Al/A2 (7.32) Convergent pipe ... losses in pipe lines 125 P P -+ - v: = -+ -+ P9 29 h, 29 P9 Therefore €72 - PI - - P9 hs 29 (7.29) Putting pzth p for the case where there is no loss, for P2th P - 0: PS - 0: (7.30) 29 The pressure ... equation of Blasius: A = 0.3164Re-’I4 (Re = x lo3 x lo’) (7.7) equation of Nikuradse: 1= 0.0032 0.221Re-0.237 (Re = IO5 x lo6) (7.8) equation of K6rmin-Nikuradse: - - + - = 1/[2loglO(Re4) 0.812 (Re...

Introduction to fluid mechanics - P8

... (8.6) and (8.7) (-) v =- A 2'3i1,2 n s Q = -1 i A5/3 - ll2 n s2I3 A = r2(;) - ?cos(;) = r2(e- sin e) sin(;) s = re ( m = - 1-2 r si:e> i.e n -T)] Z( 1-7 ) sin 'I3 v=-i112[;(1 Q = -i'121 n sine 'I3 ... cross-sections are uniform and whose banks are covered with wild grass Bending river with large stones and wild grass 0.01 0-0 .013 0.01 2-0 .018 0.01 3-0 .017 0.01 5-0 .01 0.01&0.020 0.01 7-0 .030 0.02 8-0 .035 ... masonry Non-finished concrete Concrete with exposed gravel Rough masonry Both sides stone-paved but bottom face irregular earth Deep, sand-bed river whose cross-sections are uniform Gravel-bed river...

Introduction to fluid mechanics - P9

... Bernoulli’s equation produces the following result: u2 Pd +P2 +2 pm -= p P-Pm= - -Po, PU2/2 p(U2 - Ui) (1 -4 sin28) - pu’ - -4 sinz0 (9.6) The drag of a body 151 Table 9.2 Drag coefficients for ... Drag and lift L=2 -( p-p,)rodBsin8 1n/2 ( I', u+roo = - r o p u r - 2U sin [I -XI2 (k) sin dB = - r o p U r [l - r w - z4s r n B - s i n io -4 2 U = 2m$opU = 27cr,up~ sinBd8 (9.31) The circulation ... I=, ro rdF =-ppw’r; nf (9.26) Now, putting the friction coefficient at the cylindrical part of the disc to f and the resistance acting on it to F, Ff =r- 2zr0b P(row)2 Torque T2 due to this surface...

Introduction to fluid mechanics - P10

... = [L-’MT-’][L-3M]“[L T-’]’[L]” - L 1-3 x+y+zMl+xT-l-y (10.5) i.e L: - I - ~ x + Y + z = O M: T: l+x=O -l-y=O Solving the above simultaneously gives x =-1 y =-1 z =-1 Substituting these values into ... the first non-dimensional group n, formed with D, is n1 = DpxUydz= [LMT-2][L-'M3x[LT-']y[L]' - L 1-3 x+y+zMl+xT-2-y ' (10.3) In general the basic dimensions in dynamics are three - length [L].mass ... Sphere in uniform flow i.e L: - x + y + z = O M: l+x=O T: -2 -y=0 Solving the above simultaneously gives x =-1 y =-2 z =-2 Substituting these values into eqn (10.3), then n, =- D (10.4) p U2d2 Next, select...

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