6. What is the complex conjugate function of: (a). F 10 +30i 10 ein, 10 ei7x...
6 Ivalue: 15-3 marks each] Consider the perturbation theory expression for the wave function corrected to first order Ψ(0) O)(O) 7t Briefly explain what the following terms in the above equation are a) Ψη (also state what the subscript, n, refers to) b) A' c) Ψ(0) (also what does the superscript, (0), refer to) d) Σ'nen what are we summing over? Ψ(0).Avp(0).dτ (Describe what this represents as a whole. Do (O)_(O)not explain the meaning of each individual term) nm
Suppose at a certain time to the wave function is, Ψ(x,6) N for all x between the values ofx = 1 cm and x = 2 cm. For all values ofx outside the interval [12] the wave function is zero. a) Normalize the wave function. (Solve for N). Pay attention to units! b) Sketch the probability density V(x,/,)(x, as a function of x c) What is the probability of finding the electron between 1.5 cm and 2.0 cm? d) What...
6. The Particle in a Box problem refers to a potential energy function called the infinite square well, aka the box: ; x < 0 (Region I) V(x) = 0 : 0 L (Region II) x x >L (Region III) Let's investigate a quantum particle with mass m and energy E in this potential well of length L We were unable to transcribe this image6d (continued) write down an equation relating ψ, (x = 0) to ψ"(x I and II....
Consider an electron whose wave function is ?(r,0,?)-- e* sin ? + cos ?)f(r). 47t where I (rrr2dr-| , and ?, ? are the azimuth and polar angles, respectively. (i) Rewrite the wave function in terms of the appropriate spherical harmonics. (4 marks) (ii) What are the possible measurement results of the z-component L, of the angular momentum of the electron in this state? (6 marks) (iii) Calculate the probability of obtaining each of the possible results in part (i)....
find the first three nonzero terms of the Maclaurin exapnsion kf the function. f(x)=7 sin x Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 7 sinx What is the first nonzero term of the Maclaurin expansion of f(x) = 7 sin x? 囗 What is the second nonzero term? What is the third nonzero term? Find the first three nonzero terms of the Maclaurin expansion of the function. f(x) = 7 sinx What...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
how do u do 6? F-'(C-D)= F-'(C)-F-'(D). 4. (10 points) In following questions a function f is defined on a set of real numbers. Determine whether or not f is one-to-one and justify your answers. (a) f(x) = **!, for all real numbers x #0 (6) f(x) = x, for all real numbers x (c) f(x) = 3x=!, for all real numbers x 70 (d) f(x) = **, for all real numbers x 1 (e) f(x) = for all real...
Feedback: -Check the units carefully, particularly inside the trig function. Hints: -What function describes a wave traveling in the positive x-direction that starts with a positive displacement of smax? -Be very careful how you calculate this - if you approximate π as 3.14 you may not be accurate enough, since you are evaluating a trig function of a very small value. -Watch the units - your calculate must be set in radians! Smax (13%) Problem 6: A periodic vibration at...
5. (10 points EC) BONUS QUESTION. A "sine-hump" wave is determined by the function 儡) f(t) = b sin ( Tt - bSin on the interval 0, 2a), and is then made into a periodic function across the entire t-axis by setting f(t - 2an) -f(t), for every n Z. A picture of this function for the case a 1 and b- 4 is shown below. Show by direct computation that the Laplace transform of the "sine-hump" wave described here...
Al. Practice with complex numbers: Every complex number z can be written in the form z r + iy where r and y are real; we call r the real part of z, written Re z, and likewise y is the imaginary part of z, y - Im z We further define the compler conjugate of z aszT-iy a) Prove the following relations that hold for any complex numbers z, 21 and 22: 2i Re (2122)(Re z) (Re z2) -...