Time 10.00 Function: Y(x) (x)+2(x) Two waves: set values Wave packet: set values Please read this page, follow the directions, and answer the questions posed. a. Where is the wave located? b. Keep k₂ the same and choose k₁ = 8.0 rad/m. Now, there is a localized packet. What is the uncertainty in x (measure the distance from one zero amplitude to the next)? What is the uncertainty in k (Ak = |k1 - k2|)? What is the uncertainty in x and the uncertainty in kfor part (a)?
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- Q1. Consider the non-normalized waves packet for a particle in one-dimension is given as following: а ¥1(x) = N8) otherwise 2(x) = 8Ne-(x-x,)²/a² ¿ikox (a) Calculate (x). (P). (x²). (P²).1 W:0E I VIO.Iau.cuu.3a *Problem 1.5 Consider the wave function ¥ (x, t) = Ae-Alxle-iwt where A, 2, and w are positive real constants. (We'il see in Chapter 2 what potential (V) actually produces such a wave function.) (a) Normalize Y. (b) Determine the expectation values of x and x2. 12A good mathematician can supply you with pathological counterexamples, but they do not arise in physics; for us the wave function always goes to zero at infinity. Section 1.5: Momentum 15 (c) Find the standard deviation of x. Sketch the graph of |4|², as a function of x, and mark the points ((x)+o) and ((x) – o), to illustrate the sense in which o represents the "spread" in x. What is the probability that the particle would be found outside this range?Recall that the 2D Fourier transform essentially maps an image into a collection of patterns. Consider the following k-space coordinates and sketch the pattern they represent. a. k, = kŷ b. kz = 2k (0.5 & + 9) c. kz =2 V3 Take the constant k to represent a pattern with a periodicity of that of the lines on a piece of notebook paper, and scale each of them appropriately.
- QUESTION 1 The propagation of uncertainty formula for the equation y = ax^2 is (Aya) +(Ayx) where Aya = (ax²) – ((a + Sa)x²).and .Ayx = (ax) - (a(x+ 5x)²) and. The values Sa and 5x are the uncertainties on a and x respectively. If a = -0.7 +/- 0.7 and x = -19+/-0.8 then what is the uncertainty on y? 14.5A particle is described by the following function: A for 1Q10 What is the significance of the wave function?Normally measurement uncertainty is used to represent of a measurement result? Select one: O a. dispersion O b. The half width of the distribution interval tion O c. error O d. precision The measurement error is defined as AX=X-Xo where Xo is the true value of a physical quantity. X is the measured value of the physical quantity, AX is also known as "absolute error" What is the correct understanding to absolute error? Select one: Oa An absolute error indicates the absolute value of the error Ob Absolute eror is the difference between the measured value and the true value. O e Absolute error indicates that the error is always positive. O d. Absolute eror indicates that the magnitude of an eror is certain.Q.1 Suppose that a cruise missile under test is moving horizontally at M= 2 in the atmosphere at an elevation of 305m above the earth's surface. How long dose it take for an observer on the ground to hear the disturbance from the instant when it is directly overhead? Assume standard atmosphere (15°C). 02 Air at a temperrature of -10°C lows through a supersonie wind tunnel A shadoweranh photogranh of the lowQ1: Under several simplifying assumptions, an analog of Fourier's law can be represented in one-dimensional form as: AP D=-8 dx where D is called the electric flux density vector, ɛ = permittivity of the material, and V = electrostatic potential. Similarly, a Poisson equation for electrostatic fields can be represented in two dimensions as: a2 V a2 V + ayQ1. Consider the non-normalized waves packet for a particle in one-dimension is given as following: 8N ¥,(x) = otherwise V2(x) = 8Ne-(x-x,)²/a² eikox (a) Calculate (x). (P). (x²). (P²).HOMEWORK, FINAL EXAM, ADVANCED SOLID STATE PHYSICS I 1. What are the types of the diffraction? Explain in detail. (Kırınım türleri nelerdir? Detaylı açıklayın.) 2. Explain in detail. (Ayrıntılı olarak açıklayın.) a) Classical theory of heat capacity of solids (Katıların ısı kapasitesinin klasik teorisi) b) Einstein theory of heat capacity of solids (Katıların Einstein ısı kapasitesi teorisi) c) Thermal conduction by phonons (Fononlarla ısı iletimi) 3. Atomic packing factor. (Atomik paketleme faktörü.) Find the atomic packing factor for Simple Cubic (SC). (Basit kübik (SC) için atomik paketleme faktörünü bulunuz.). Find the atomic packing factor for Diamond Structure .(Elmas yapı için atomik paketleme faktörünü bulunuz.) 4. Explain or show the options given below. (Aşağıda verilen şıkları açıklayın veya gösteriniz.) a. Calculate the interplanetary distance of (111) and (210) in the Tetragonal Crystal system Tetragonal Kristal sisteminde (111) ve (210) düzlemler arası uzaklığı…According to the principles of quantum mechanics, every particle acts like a wave. To demonstrate this, a helium nucleus is shown to exhibit interference as it passes through a double-slit. The helium nucleus has a mass of 6.64 x 10^-27 kg and its speed is 500.0 m/s when is passes through the slits. a. What is the wavelength of the wave associated with the helium nucleus in nanometers? b. If the slits are seperated by 1.00 nm and the distance from the slits to the detector (effectively, the "screen") is 15.0 cm, what is the distance, in centimeters, from the central maximum to the first-order maximum of constructive interference? c. If the uncertainty in the velocity of the helium nucleus is 18 m/s, what is the uncertainty in its position, assuming a simultaneous measurement?SEE MORE QUESTIONS