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2. Determine whether the following function satisfies the wave equation. Y(x,t)= Ae (kr-at)
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
check whether the function E(x,t)= Asin(kx^2-wt^2) satisfies the wave equation. if so, find the wave speed....
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
PrOBleM: SoLuTiONS To THE WAvE EQuATION a) By direct substitution determine which of the following functions...
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....
Show that a function w(x, y) = cos(2x + 2ct) satisfies wave equation.
Show that a function w(x, y) = cos(2x + 2ct) satisfies wave equation.
Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for x < 0.
A fellow student proposes that a possible wave function for a free particle with mass \(m\) (one for which the potential-energy function \(U(x)\) is zero ) is$$ \psi(x)=\left\{\begin{array}{ll} e^{-k x}, & x \geq 0 \\ e^{+\kappa x}, & x<0 \end{array}\right. $$where \(\kappa\) is a positive constant. (a) Graph this proposed wave function.(b) Determine the energy of the particle if the proposed wave function satisfies the Schrödinger equation for \(x<\)0.(c) Show that the proposed wave function also satisfies the Schrödinger equation...
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a,...
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a, B are arbitrary constants, i is the unit imaginary number. b) Find the wave speed where a = 1, B = 4, and A-3.
Consider the following wave function: y(x, t) = cos(kx - omega t). a. Show that the...
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).
The wave equation can be written as:∂^2 y/∂x^2 = 1/v^2 (∂^2 y /∂t^2) where y =...
The wave equation can be written as:∂^2 y/∂x^2 = 1/v^2 (∂^2 y /∂t^2) where y = y(x,t) has units of meters, x is also in meters, and t is in seconds. (a) Show explicitly that the function y(x,t) = ymsin(kx)cos(wt) satisfies the wave equation (6 points). (b) Is the function for y = y(x,t) describe a traveling wave? You must explain your answer to get full credit (2 points). 8. On a winter day with a temperature of Tc, the...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x,...
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
2. Determine whether the following function satisfies the wave equation. v(x,t)= 4e(in-a)
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....
Show that a function w(x, y) = cos(2x + 2ct) satisfies wave equation.
P(x,t) = Aeixe-ißt a) Show that the above function is a wave by showing that it satisfies the wave equation. A, a, B are arbitrary constants, i is the unit imaginary number. b) Find the wave speed where a = 1, B = 4, and A-3.
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).
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
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