Show whether the following functions are wave functions or not.1. У(х, t)еxp(ikx)= A-exp (i(ot-Ф))кЗх3-0313-3kоxt(kx-ot)-iф))2 У(х, t)3. y(x, t)Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip))Аехр (i(-kx? + оt))

A wave function is a function which can be expressed in the form yx,t=fkx±ωt where the function fu…

Answered: Show whether the following functions…

Show whether the following functions are wave functions or not. 1. У(х, t) 3D А exp(ikx) = A- exp (i(ot-ф)) 2 y(x, t) = Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip)) Аехp(1(-kx? + ot)) 3. y(x, t) =

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

See similar textbooks

Related questions

Q: 4. Find the work done by the force field F (x,y) = (x + y)î + (xy)ĵ in moving a particle along the…

A: The force field is given by F→ = x+yi^+xyj^ The end points of the straight line along which the…

Q: Show that cos(wt – B), cos wt , sin wt are linearly dependent functions of t.

Q: Show that the u = f (x + ct) + F(x – ct) satisfies the wave equation in one-dimensional space.

A: By doing partial derivatives we can prove

Q: (c(2z+y), %3D ue of c in the joi F of W.

Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P…

Q: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at (12,12,12)…

Q: An elastic string is stretched between two points 40 cm apart. Its center point is displaced 1.5 cm…

Q: Show that f(x, y) =(Aekx + Be-kx )(Ce2ky + De−2ky) is a solution of the wave equation ∂2f/∂y2−…

Q: A particle moves in a path defined by vector-valued fanction FH)= (4)i +(zt-3)j + ( 3t - 3t) K ,…

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

A: The position vector of the particle is given by r(t) = 2t2, t3, -1

Q: 2. Calculate the directional derivative of the scalar field U(x, y,z) at the point M,, along the…

A: Given that : U=xz3y-x3y=xz3y-x32y12 The gradient will be calculated as :…

Q: An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx²…

A: Let us consider the wave equation ∂2u∂t2=∂2u∂x2, 0≤x≤1, t≥0 and L=∆x=0.25; K=∆t=0.1 Consider x=ih…

Q: rotational velocity field v = ⟨0, 10z, -10y⟩ . If a paddle wheel is placed in the plane x + y + z =…

A: Curl F can be the measure tendency of F to produce rotation. First a paddle wheel is kept in such a…

Q: Solve the wave equation in two dimensions Utt = v²u u (x, y, 0) = sin 4y U (x, y, 0) = cos xcos3y…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: 1. Given the time_Varying position Vector x iat+jbt2+Kct z where ast,b=2,andc=3_are Gnstants. hind…

A: Given : a=1, b=2, c=3 x = iat+jbt2+kct3

Q: Find the work done by the force field F(x, y, z) = on particle that moves along the line segment…

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the…

A: Given a string of length 15 cm is stretched between two points. We have to obtain the differential…

Q: Solve the wave equation on the half line with the Utt – cʻuxx = 0, x> 0, t > 0 и, (0, 1) %3D h(),…

A: Given the wave equation is utt-c2uxx=0, x>0, t>0ux(0,t)=h(t),…

Q: The motion of string deflection u, can be expressed by the one-dimensional wave equation, shown in…

A: Given that: ∂2u∂t2=c2∂2u∂x2 ...1 c2=Tp, Where T=Tension in string p=mass per unit length of string…

Q: Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P…

Q: 3. Verify that u(r,t) = sin(r - at) satisfies the wave equation:

A: To verify that ux, t=sinx-at satisfies the wave equation ∂2u∂t2=a2∂2u∂x2

Q: 2的在年

Q: =) Find the directional derivative at the point P = (2, 1, 1) of the scalar function in the…

Q: 2. Prove that the directional derivative of f(x, y, 2) = ry sin z at (1,2, ) in the direction v = i+…

A: Given: fx,y,z=xy sinz x,y,z=1,2,π2 direction v=i+2j+2k Differentiate the…

Q: Q2) Find the directional derivative of F(x,y,z)= sin(yz)+In(x³) at the point(1,1,7) in the direction…

A: This question is related to vectors, we will use gradient of function to solve this.

Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

Q: Solve using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)

Q: Suppose T(x, y, z) is the temperature at position (x, y, z) and suppose u is a unit vector pointing…

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

Q: A uniform solid sphere of radius r = 0.570 m and mass m = 14.5 kg turns counterclockwise about a…

Q: 5- Find the solution of the following wave equation using the method of separation of variables.…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

Q: 10. Find the work done by the force F=vx +2y y - 7 for a particle that moves between points (-1,0,1)…

Q: The gradient vector of g(x, y) = at (√√2,-1) is Vg(√2, -1) is equal to Select one: O True O False -

A: Given: The gradient vector of g(x,y)=x22-y22 at (2,1) is ∇g(2,1) is equal to <2,1>

Q: Calculate the directional derivatives of the function f(x,y) = x² – y? in the direction of the…

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

Q: Consider a vibrating guitar string of length L = 648mm that satisfies the wave equation Uxx = Utt, 0…

A: Given below clear explanation

Question

Show whether the following functions are wave functions or not.
1. У(х, t)
еxp(ikx)
= A-
exp (i(ot-Ф))
кЗх3-0313-3kоxt(kx-ot)-iф))
2 У(х, t)
3. y(x, t)
Aexp(i(k³x³-w³t³-3kwxt(kx-wt)-ip))
Аехр (i(-kx? + оt))

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Harmonic Motion$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Suppose z is given implicitly by the equation ln (yz2) + x3z = −1 in a neighborhood of the point P (1, 1), in which z = −1. The value of the directional derivative of z at P in the direction of the vector w = (−1, 1), corresponds to: the answers are in the first attached image
What does it mean for the differentiability of a function if only one of the Cauchy-Reimann equations (Ux = Vy and Vx = -Uy) holds?
Suppose z is given implicitly by the equation ln (yz2) + x3z = 1 in a neighborhood of the point P (1, 1), in which z = 1. The value of the directional derivative of z at P in the direction of the vector w = (1, −1), corresponds to:
What did you write for the wave equation at the beginning? is that the same as Schrodinger's Eq.?
Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1, −2), in which z = −2. The value of the directional derivative of z at P in the direction of the vector w = (−3, −4), corresponds to:
Find a vector equation for the tangent line to the curve of intersection of the cylinders x2+y2=25 and y2+z2=20 at the point (3, 4, 2).
How would I go about deriving this with respect to the parameter mu?
4 Find the directional derivative of f (x,y)= 2x^2 y^2 -3xy at the point (1,-1) in thedirectiona. of vector v =<4,3> and toward the origin.
for wave equation, seperation of vairables u(x,t)=X=(x)T(t)
Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = y - 2x , (1,0)
Sketch the direction field of the differential equa tion.Then use it to sketch a solution curve that passes through thegiven point. y' = x - xy , (1,0)
Show that ¥(x,t)= Asin(wt+kx) describes a wave motion