![Suppose at a certain time to the wave function is, Ψ(x,6) N for all x between the values ofx = 1 cm and x = 2 cm. For all values ofx outside the interval [12] the wave function is zero. a) Normalize the wave function. (Solve for N). Pay attention to units! b) Sketch the probability density V(x,/,)(x, as a function of x c) What is the probability of finding the electron between 1.5 cm and 2.0 cm? d) What is the probability of finding the electron between 1.1 cm and 1.7 cm? Suppose at a certain time to the wave function is Ψ(x,to) = Ne-sn). for all x, where /is equal to I Angstrom (- 10 cm) a) Normalize the wave function, (Hint Jor-ar, tr = r/a) b) Sketch the probability density as a function of x](http://img.homeworklib.com/questions/1064b360-75a3-11ea-ac78-03166c789f3f.png?x-oss-process=image/resize,w_560)
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Suppose at a certain time to the wave function is, Ψ(x,6) N for all x between...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
Consider a wave function given by ψ(x)=A sinkx, where k=2π/λ and A is a real constant....
Consider a wave function given by ψ(x)=A sinkx, where k=2π/λ and A is a real constant. For what values of x is there the highest probability of finding the particle described by this wave function? x=nλ/2, n = 1, 3, 5,... x=nλ/4, n = 0, 2, 4,... x=nλ/2, n = 0, 2, 4,... x=nλ/4, n = 1, 3, 5,...
Problem 2 Consider the wave function Where a, λ ω are positive constants. (a) Normalize (b)...
Problem 2 Consider the wave function Where a, λ ω are positive constants. (a) Normalize (b) Determine the expectation values ofx and x; (c) Find the standard deviation ofx. Sketch the graph of 1992, as a function ofx, and mark the points (<x> + σ) and 〈X>-07, to illustrate the sense in which σ represents the "spread" in x, what is the probability that the particle would be found outside this range?
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...
Please include explanations I. The graph shows the wave function ψ(x) of a particle between x =0 nm and x-2.0 nm. The cvx 0to 2.0 nm probability is zero outside of this region. In other words,p(x) -...
Please include explanations I. The graph shows the wave function ψ(x) of a particle between x =0 nm and x-2.0 nm. The cvx 0to 2.0 nm probability is zero outside of this region. In other words,p(x) - a) Find c, as defined by the figure. P(x) b) What is the probability of finding a particle between 1.0 nm and 2.0 nm? c) What is the smallest range of velocities you could find for an electron confined to this distance of...
A particle is represented by the following wave function: ψ(x) =0 x<−1/2 ψ(x) =C(2x +...
A particle is represented by the following wave function: ψ(x) =0 x<−1/2 ψ(x) =C(2x + 1) −1/2 < x < 0 ψ(x) =C(−2x + 1) 0 < x < +1/2 ψ(x) =0 x > +1/2 (a)Evaluate the probability to find the particle between x=0.19 and x=0.35. (b) Find the average values of x and x2, and the uncertainty of x: Δx=√(x2)av-(xav)2 xav= (x2)av= Δx =
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of fin...
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of finding 1-0? (c) Construct ψ(r, θ, φ) and another wave function with the same values of n and (azimuthal) quantum number, m+1 (d) Calculate the most probable value of r for an electron in the state corresponding to ψ(r, θ, φ) 1, but with...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x)...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
3. An atom is in a time-independent one-dimensional potential well. The system's spatial wave function is ψ(x)-Asin(2mz/L) for 0 < x < L and zero for all other z. What is the average of...
3. An atom is in a time-independent one-dimensional potential well. The system's spatial wave function is ψ(x)-Asin(2mz/L) for 0 < x < L and zero for all other z. What is the average of the position operator? For which o is the probability that the atom is located in the interval [xo 0.01L, o 0.01L] largest?
3. An atom is in a time-independent one-dimensional potential well. The system's spatial wave function is ψ(x)-Asin(2mz/L) for 0
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0,...
The initial wave function of a free particle is: Ψ(x,0) = A, for |x| = 0, otherwise where a and A are positive real numbers. The particle is in a zero (or constant) potential environment since it is a free particle a) Determine A from normalization. b) Determine φ(p) = Φ(p,0), the time-zero momentum representation of the particle state. What is Φ(p,t)? Sketch φ(p). Locate the global maximum and the zeros of φ(p). Give the expression for the zeros (i.e.,...
3. At time t-0 a particle is represented by the wave function A-if 0 < x<a ψ(x,0) = 0 otherwise where A, a, and b are constants. a) Normalize ψ(x,0). b) Draw (x,0). c) Where is the particle most likely to be found at t-0? d) What is the probability of finding the particle to the left of a? e) What is the expectation value of x?
Problem 2 Consider the wave function Where a, λ ω are positive constants. (a) Normalize (b) Determine the expectation values ofx and x; (c) Find the standard deviation ofx. Sketch the graph of 1992, as a function ofx, and mark the points (<x> + σ) and 〈X>-07, to illustrate the sense in which σ represents the "spread" in x, what is the probability that the particle would be found outside this range?
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...
Please include explanations I. The graph shows the wave function ψ(x) of a particle between x =0 nm and x-2.0 nm. The cvx 0to 2.0 nm probability is zero outside of this region. In other words,p(x) - a) Find c, as defined by the figure. P(x) b) What is the probability of finding a particle between 1.0 nm and 2.0 nm? c) What is the smallest range of velocities you could find for an electron confined to this distance of...
Consider a wave function for a hydrogen-like atom: 81 V πα3 a) Find the corresponding values of the quantum num bers n, 1, and m. (b) By measuring the angular momentum, what is the probability of finding 1-0? (c) Construct ψ(r, θ, φ) and another wave function with the same values of n and (azimuthal) quantum number, m+1 (d) Calculate the most probable value of r for an electron in the state corresponding to ψ(r, θ, φ) 1, but with...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
3. An atom is in a time-independent one-dimensional potential well. The system's spatial wave function is ψ(x)-Asin(2mz/L) for 0 < x < L and zero for all other z. What is the average of the position operator? For which o is the probability that the atom is located in the interval [xo 0.01L, o 0.01L] largest?
3. An atom is in a time-independent one-dimensional potential well. The system's spatial wave function is ψ(x)-Asin(2mz/L) for 0
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