1. Which of the following could NOT possibly be wave functions and why? Assume 1-D in each case. ...
1. Which of the following could NOT possibly be wave functions and why? Assume 1-D in each case. (Here C is a normalization constant) If any of these are valid wave functions, calculate C for those case(s). Where is the particle most likely to be?
a) Ψ (x) = C x exp (-x) for x > 0. Ψ (x) is zero everywhere else.
b) Ψ (x) = C [exp(2x) + exp(-2x)] for all x.
Homework Answers
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1. Which of the following could NOT possibly be wave functions and why? Assume 1-D in each case. ...
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1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable...
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Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
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1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
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I need help with d) please help thank you
Question 1 Wave motion appears in all branches of physics. In the lectures we considered the solution of the advection equation, a first-order hyperbolic PDE. Here we consider the solution of the wave equation: c2 where c >0 is constant. , We assume all variables have been non-dimensionalised. (a) Eq. (1) has the general solution (d'Alembert, 1747): u(x,t) F(x -ct) +G(x ct), where F and G are arbitrary functions. Consider the...
Which computer based optimization technique would you recommend for each of the following objective functions? Please...
Which computer based optimization technique would you recommend for each of the following objective functions? Please justify your answer briefly in each case Powell's quartic function: (11025(r3-4)2+ (x2 - 2x3)4 +10(xi - x4)4; f(x) x 3,-1,0, 1]7; x' = (0,0,0, o]*". Fletcher and Powell's helical valley f(x) 100 (x3 100(a1, 2))2 (V+) if x1 > 0 arctan where 2T0(x1,2) 2 TTarctan if a 0 (-1,0, 0; x 1,0,07 х0 c) A non-linear function of three variables: 1 f(x) TT23+exp sin...
b. Where is the particle most likely to be found? Explain why. Answer: x = 0 c. Find the probability to find the particle in the region -0.1a < x < 0.la . Answer: P(-0.1a < x < 0.1a) = 0.18625 d. Find the following expectation values: (x) and (x2) Answer: (x) = 0, (x2) = 0.14286 a2 1) A particle's wavefunction at time t=0 is given by: xs-a (x) = {A GE for-asxsa for a Below are the plots...
1. Suppose we didn't actually know the wave functions for a particle in a box. Reasonable guesses for the ground- and first-excited-state wave functions might be functions of the form 1 = a y (1 - y) 02 = by (y-c)(y-1), where y = (x/L), L is the length of the box, and a, b, and care constants. (a) These functions have quite a number of features that make them sensible guesses. Sketch both functions and list these special features....
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions satisfy the wave equation 1. g(z, t)-A cos(kr - wt) where A, k, w are positive constants 2. h(z,t)-Ae-(kz-wt)2 where A, k, ω are positive constants 3. p(x, t) A sinh(kx-wt) where A, k,w are positive constants 4. q(z, t) - Ae(atut) where A,a, w are positive constants 5. An arbitrary function: f(x, t) - f(kx -wt) where k and w are positive constants....
Problem 1. Wave function An electron is described by a wave function: for x < 0 *(z) = { ce Ce-s/1(1 – e-3/4) for x > 0 : where I is a constant length, and C is the normalization constant. 1. Find C. 2. Where an electron is most likely to be found; that is, for what value of x is the prob: bility for finding electron largest? 3. What is the average coordinate 7 of the electron? 4. What...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Answers can be more than one:
VII. (12pts) Consider the following potential energy: region 1: U(X) = U. x < 0 region 2: U(X) = 0 0<x</ Uo region 3: U(x) = U. x>L ТЕ where U. >0. We want to consider a particle with energy E such that 0 < E<Uo. There are two possible forms for the wave function that might be used to represent the particle: (x) = 4 sin kyx+ B, coskx v(x) = 4e** +...
I need help with d) please help thank you
Question 1 Wave motion appears in all branches of physics. In the lectures we considered the solution of the advection equation, a first-order hyperbolic PDE. Here we consider the solution of the wave equation: c2 where c >0 is constant. , We assume all variables have been non-dimensionalised. (a) Eq. (1) has the general solution (d'Alembert, 1747): u(x,t) F(x -ct) +G(x ct), where F and G are arbitrary functions. Consider the...
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