If the wave function of a system is U(r)=1/VTt (1/a)³/² exp(-r/a) , from the period r=0 to r=o, where a is a constant, the average dimension of this function is: a/ 1.25a b/ 2.5a C/1.5a d/0.5a
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- Most real time clock chips use 32.678 KHz crystals (2^15), Why clock chips of 2^12 Hz or 2^18 Hz are not considered just as good?In 2019, the International Committee for Weights and Measures adopted a new set of definitions for the fundamental units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length (m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system: Quantity Symbol Units Transition Frequency of Cesium 133 Av s-1 kg - m?/s m/s Planck's Constant h Speed of Light Use dimensional analysis to determine the combination of these three parameters that will define the base units of the SI system. (a) What combination of h, c, and Av defines a second? (b) What combination of h, c, and Av defines a meter? (c) What combination of h, c, and Av defines a kilogram? You only need to find the combination of h, c, and Av that has the right units. Your answer should not involve any numerical values.Let x(t) = [4 cos(100t) + sin(100t) + e-50t cos(50√19t)]. Then deduce that (a) x(t) solves (t) + 10x'(t) + 5000×(t) = 400 cos(100t). 10 (b) the steady-state solution from the given x(t). (c) Plot x(t) & xp(t) on the same set of axis and estimate the time required for the transient motion to effectively disappear.
- 0, f(x) = -TA PERIODIC FUNCTIONS f(t) WITH PERIOD 2TT IS DEFINED BY f(t) = t² + t (-πa) Determine the quantum mechanical operators for the following: Lx = ypz - ZPy That is, find Îx = ŷpz - 2py where x = x êx = ħa i əx Ly = Zpx -xPz Ly = 2px - xpz ŷ = y Py = ћд і ду 2= Z Lz = xpy - ypx L₂ = xpy - ŷêx Pz = ћд і дz(2nx sin \1.50. 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = sin(ny) sin 2.00. What is the energy of the system? O 6h?/8m O 4h²/8m O 3h2/8m O none are correcta) Determine the quantum mechanical operators for the following: Lx=yPz - ZPy That is, find Îx = ŷêz - 2py where x = x êx = ћд і дх Ly = Zpx - xPz Îy = 2px - xôz ŷ = y Py = b) Determine the commutator i.e. [θ‚΂] - - = x 'y ħ a і ду 2 = z Lz = xpy - ypx Û₂ = âÔy – ŷÂx êz = (΂΂¸ – θÎx)ƒ(xx.2) = ? L y ħ ə і дzQuestion 12/ 13 An electron mnoves in a straight line with constant speed y= 1.1 x10" m's which has been measured with precision of 0.10%. What is the maximum possible precision in which its position could be measured? (h= 6.62 x 10 34 m kg /s; m= 9.11 x 10 31 kg)View of a one-dimensional harmonic oscillator system on the x axis of a charged particle q with an energy spectrum of En = (n + ½)ħw. The system is then disturbed by an oscillating electric field as a wo• function of time t such that the disturbance potential energy can be expressed as untuk t o 0 v (t) = {_q {-9€x sin wt e-t With & electric field amplitude. (notes : untuk means for) a. Calculate the transition probability from state n to state m. b. State which transitions n → m are allowed and which are not allowed to occur. c. Explain what happens if w → wo and/or → 0. [Hint: Use the create and annihilate operators to enumerate Matrix elements.]A certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?A particle moving in one dimension has the wave function Y(x,t) = Aeli(ax-bt)] %3D where a and b are constants. What is the potential field V(x) in which the particle is moving?SEE MORE QUESTIONSRecommended textbooks for youPhysics for Scientists and Engineers: Foundations…PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPhysics for Scientists and Engineers: Foundations…PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning