. Using the wave equat check 7 whether the following function is a wave or not...
3) Prove that V(e)=A is a solu too to the wave equat,ON d 2
check whether the function E(x,t)= Asin(kx^2-wt^2) satisfies the wave equation. if so, find the wave speed. if not explain
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
Consider a wave-packet of the form y(x) = e-x+7(204) describing the quantum wave function of an electron. The uncertainty in the position of the electron may be calculated as Ax = V(x2) – ((x))2 where for a function f(x) the expectation values () are defined as (f(x)) = 5-a dx|4(x)/2 f(x) so dx|4(x)2 Calculate Ax for the wave packet given above. (Hint: you may look up the Gaussian integral.]
****Using c++ (Check Substrings) Write the following function to check whether string s1 is a substring of string s2. The function returns the first index in s2 if there is a match. Otherwise, return -1. int indexOf(const string& s1, const string& s2) Write a test program that reads two strings and checks whether the first string is a substring of the second string.
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...
2. Determine whether the following function satisfies the wave equation. Y(x,t)= Ae (kr-at)
Problem 7: Finite Square Well Sketch a possible wave function v(x) corresponding to a particle with energy E in the potential well shown below. Describe for eachregion why the wave function is oscillatory or decaying. ski R1 Region 2 R3 Region 4 R5
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
please explain the four conditions of an acceptable wave function.. and how to use that. For rxample I have a function exp(ax^2). I want to check whether this is an acceptable wave function or not. how to proceed?