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Consider a particle confined to one dimension and positive r with the wave function 0, z<0...
Consider a particle confined to one dimension and positive z with the wave function 0 where...
Consider a particle confined to one dimension and positive z with the wave function 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: f) Calculate the expectation value of the momentum, (p) via the canonical expression -0o g) Calculate the expectation value of (p) via the canonical expression h) Use your results for(i) and (pay to calculate the variance in...
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0...
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: a) Find the normalization constant N. What are the units of your result and do they make sense? b) What is the most probable location to find the particle, or more precisely, at what z...
Consider a particle which is confined to move along the positive x-axis, and that has a...
Consider a particle which is confined to move along the positive x-axis, and that has a Hamiltonian where is a positive real constant having the dimensions of energy. Find the normalized wave function that corresponds to an energy eigenvalue of . The function should be finite everywhere along the positive x-axis and be square integrable. H = 8
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.,...
A quantum object confined to a container of dimension a is described by this unnormalized wave...
A quantum object confined to a container of dimension a is described by this unnormalized wave function: this wave function Phi(x)n = A(1-x/a) where A is the normalization constant. Given that 0 ≤ x ≤ a, what is the value of the constant A?
Consider a particle of mass m that is described by the wave function (x, t) =...
Consider a particle of mass m that is described by the wave function (x, t) = Ce~iwte-(x/l)2 where C and l are real and positive constants, with / being the characteristic length-scale in the problem Calculate the expectation values of position values of 2 and p2. and momentum p, as well as the expectation Find the standard deviations O and op. Are they consistent with the uncertainty principle? to be independent What should be the form of the potential energy...
A particle moving in one dimension is described by the wave function ...
A particle moving in one dimension is described by the wave function$$ \psi(x)=\left\{\begin{array}{ll} A e^{-\alpha x}, & x \geq 0 \\ B e^{\alpha x}, & x<0 \end{array}\right. $$where \(\alpha=4.00 \mathrm{~m}^{-1}\). (a) Determine the constants \(A\) and \(B\) so that the wave function is continuous and normalized. (b) Calculate the probability of finding the particle in each of the following regions: (i) within \(0.10 \mathrm{~m}\) of the origin, (ii) on the left side of the origin.
Problem 3: A free particle of mass m in one dimension is in the state Hbr...
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
A quantum mechanical particle confined to move in one dimension between x =0 and x -L...
A quantum mechanical particle confined to move in one dimension between x =0 and x -L is found to have a state described by the wavefunction 2T (a) Determine the constanfA such that the wavefunction is normalized./ (b) Using the result of part (a), find the probability that the particle will be found between x 0 and x L/3
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.
Consider a particle confined to one dimension and positive z with the wave function 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: f) Calculate the expectation value of the momentum, (p) via the canonical expression -0o g) Calculate the expectation value of (p) via the canonical expression h) Use your results for(i) and (pay to calculate the variance in...
Consider a particle confined to one dimension and positive with the wave function Nxear, x20 x<0 0 where N is a real normalization constant and α is a real positive constant with units of (length)-1. For the following, express your answers in terms of α: a) Find the normalization constant N. What are the units of your result and do they make sense? b) What is the most probable location to find the particle, or more precisely, at what z...
Consider a particle of mass m that is described by the wave function (x, t) = Ce~iwte-(x/l)2 where C and l are real and positive constants, with / being the characteristic length-scale in the problem Calculate the expectation values of position values of 2 and p2. and momentum p, as well as the expectation Find the standard deviations O and op. Are they consistent with the uncertainty principle? to be independent What should be the form of the potential energy...
Problem 3: A free particle of mass m in one dimension is in the state Hbr Ψ(z, t = 0) = Ae-ar with A, a and b real positive constants. a) Calculate A by normalizing v. b) Calculate the expectation values of position and momentum of the particle at t 0 c) Calculate the uncertainties ΔΧ and Δ1) for the position and momentum at t 0, Do they satisfy the Heisenberg relation? d) Find the wavefunction Ψ(x, t) at a...
A quantum mechanical particle confined to move in one dimension between x =0 and x -L is found to have a state described by the wavefunction 2T (a) Determine the constanfA such that the wavefunction is normalized./ (b) Using the result of part (a), find the probability that the particle will be found between x 0 and x L/3
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