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3. Consider the wave function ψ(x)- 슬 읔 ets, where σ s a real valued constant...
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 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,...
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.,...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness...
Consider the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use...
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...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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 the harmonic oscillator wave function 1/4 where α = (-)"*. Here k, is the stiffness coefficient of the oscillator and m is mass. Recall that the oscillation frequency iso,s:,k, / m In class we showed that Ψ0(x) Is an eigenfunction of the Hamiltonian, with an eigenvalue Eo (1/2)ha a) Normalize the wave function in Eq.(1) b) Graph the probability density. Note that a has units of length and measures the "width" of the wave function. It's easier to use...
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...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
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