3. Parameters of an Example Wave Function An electron that is not localized in space is...
3. Parameters of an Example Wave Function
An electron that is not localized in space is described by the wave function Ψ(x, t) = A sin(kx−ωt). The kinetic energy of the electron is 1 keV. The potential everywhere is zero, i.e., V (x, t) = 0. Find k and ω. For each, provide a one-sentence description of the physical interpretation of that quantity. Hint: Start with the definitions of the wavenumber k = 2π/λ and angular frequency ω = 2πf. Next, there are two de Broglie relations to consider: λ = h/p and f = E/h.
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3. Parameters of an Example Wave Function
An electron that is not localized in space is...
Consider a wave that is represented by ψ(x, t) = 4 cos (kx − ωt). where...
Consider a wave that is represented by ψ(x, t) = 4 cos (kx − ωt). where k = 2π/λ and ω = 2πf. The aim of the following exercises is to show that this expression captures many of the intuitive features of waves. a) Consider a snapshot of the wave at t = 0. Use the expression to find the possible values of x at which the crests (maximum points) of the wave are located. By what distance are neighboring...
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish by calculating the following quantities. (Us...
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish by calculating the following quantities. (Use the following as necessary: A, K, x, ,t, h, and m.) momentum Need Help?Read ItTalk to a Tutor
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish...
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are...
A free particle moving in one dimension has wave function Ψ(x,t)=A[ei(kx−ωt)−ei(2kx−4ωt)] where k and ω are positive real constants. At t = π/(6ω) what are the two smallest positive values of x for which the probability function |Ψ(x,t)|2 is a maximum? Express your answer in terms of k.
A free electron has a wave function ψ(x)= Asin (5x1010 x) where x is measured in...
A free electron has a wave function ψ(x)= Asin (5x1010 x) where x is measured in meters. Find the electron's de Broglie wavelength the electron's momentum a. b, 3. When an electron is confined in the semi-infinite square, its wave function will be in the form Asin kx for0<x<L ψ(x)- Ce for x> L having L = 5 nm and k = 1.7 / nm. a. Find the energy of the state. b. Write down the matching conditions that the...
Dont do Part A. A localized electron at rest has a wave function ψ(x)=A exp( a22.2)...
Dont do Part A.
A localized electron at rest has a wave function ψ(x)=A exp( a22.2) with a=0.5/nm. (a) Use the results from class to quote it's space and momentum uncertainty (b) Use the static Schrödinger equation to calculate the pertinent potential, U(x).
Two wave pulses travel on a string toward each other. The wave pulses can be described...
Two wave pulses travel on a string toward each other. The wave pulses can be described as y1 = 5/(((kx − ωt)^2) 2) and y2 = −5/(((kx + ωt − 6)2 )+2)' , where k = 1 rad/m and ω = 8 rad/s. At what instant do the two cancel everywhere? (Assume x is in meters and t is in seconds.) ???s At what point do the two pulses always cancel? ???m
A transverse wave with an amplitude of 6 m, a frequency f=6.7 Hz , and a...
A transverse wave with an amplitude of 6 m, a frequency f=6.7 Hz , and a wavelength λ=6 m is traveling down a taut string. If the wave equation describing the displacement of the string at position x and time t is given by y(x,t)=Asin(kx−ωt) a.) what are the parameters A, k, and ω? b.) What is the speed of the wave traveling down the wire? m/s c.) If the tension in the wire is measured to be 6 N,...
Which statement about the wave function for a single electron is NOT correct? 1- Louis de...
Which statement about the wave function for a single electron is NOT correct? 1- Louis de Broglie postulated that the wavelength of an electron is given in terms of Planck's constant and its momentum, λ = h / p. 2- A French graduate student named Louis de Broglie first had the idea that an electron should be described as a wave. 3-The amplitude of a wave function at a particular point in space equals the probability density of finding the...
A free proton has a wave function Psi (x) = A sin (kx), where k =...
A free proton has a wave function Psi (x) = A sin (kx), where k = 1.2 times 10^10 m^-1 What is the proton's lambda? What is the proton's momentum? What is the proton's speed? Normalize Psi (x) if the wave only exists inside an infinite square well with width a = 2.1 m, (so that Psi (x) = A sin (kx) between 0 < x < a and Psi (x) = 0 otherwise).
A sinusoidal transverse wave of wavelength 19.0 cm travels along a string in the positive direction...
A sinusoidal transverse wave of wavelength 19.0 cm travels along a string in the positive direction of an x axis. The displacement y of the string particle at x = 0 is given in the figure as a function of time t. The scale of the vertical axis is set by ys = 4 cm. The wave equation is to be in the form of y = ym sin(kx - ωt + φ). (a) At t = 0, is a...
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish by calculating the following quantities. (Use the following as necessary: A, K, x, ,t, h, and m.) momentum Need Help?Read ItTalk to a Tutor
9. 1.66 points Show that the wave function ψ-A ei(kx-at) is a solution to the Schrödinger equation, given below, where k-2π / λ and U-0. 2m dz2 Accomplish...
A free electron has a wave function ψ(x)= Asin (5x1010 x) where x is measured in meters. Find the electron's de Broglie wavelength the electron's momentum a. b, 3. When an electron is confined in the semi-infinite square, its wave function will be in the form Asin kx for0<x<L ψ(x)- Ce for x> L having L = 5 nm and k = 1.7 / nm. a. Find the energy of the state. b. Write down the matching conditions that the...
Dont do Part A.
A localized electron at rest has a wave function ψ(x)=A exp( a22.2) with a=0.5/nm. (a) Use the results from class to quote it's space and momentum uncertainty (b) Use the static Schrödinger equation to calculate the pertinent potential, U(x).
A free proton has a wave function Psi (x) = A sin (kx), where k = 1.2 times 10^10 m^-1 What is the proton's lambda? What is the proton's momentum? What is the proton's speed? Normalize Psi (x) if the wave only exists inside an infinite square well with width a = 2.1 m, (so that Psi (x) = A sin (kx) between 0 < x < a and Psi (x) = 0 otherwise).
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