Homework Answers
P0 is initial momentum of a particle which cannot be measured accurately when position is measured accurately.
Hence the imaginary value of momentum iP0
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What is the physical sense of the quantity po in the expression for the wave-function: *(x)...
Problem #1 ---- -15pts- vvhat is the physical sense of the quantity Do in the expression...
Problem #1 ---- -15pts- vvhat is the physical sense of the quantity Do in the expression for the wave-function *(x) = $(x) exp(':) (x) is real? where the function
PRINT YOUR NAME (on every page) Midterm exam 32300 G-Introduction to Quantum Mechanics-Prof. Krusin Solve all...
PRINT YOUR NAME (on every page) Midterm exam 32300 G-Introduction to Quantum Mechanics-Prof. Krusin Solve all 4 problems 15pts Problem #1 What is the physical sense of the quantity po in the expression for the wave-function: Cx) (x) exp ( ipox where the function (x) is real? 25ntc
Write the expression for y as a function of x and t for a sinusoidal wave...
Write the expression for y as a function of x and t for a sinusoidal wave along a rope in the negative x direction with the following characteristics: A = 8.00 cm: lambda = 80.0 cm: f= 3.00 Hz and y(0, t) = 0 at t = 0. Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at x = 10.0 cm.
Given a real potential V(|x|), and aymptotic form of the wave function ѱ_k^+ (x)→e^(ik∙x)+f(θ,ϕ)∙...
Given a real potential V(|x|), and aymptotic form of the wave function ѱ_k^+ (x)→e^(ik∙x)+f(θ,ϕ)∙(exp(ikx))/x, Use the continuity equation and Gauss*s theorem to derive the optical theorem σ_tot=(4π/k)Imf(0) Where σ_tot is the total cross section. Discuss the physical meaning of this reult. Can you explain why it is the scattering amplitude in the forward direction (i,e, θ=0), that enters in the formula above? Can you generalize this reult if V is complex?
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.,...
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance...
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of ψι and in Problem 2.5: where ф įs some constant. Find ų,(x,t), Ux.t)12, and (x), and compare your results with what you got before. Study the special cases φ = π/2 and φ = π....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively. Derive the expression for the inner product (4) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? b) Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states [4) and (o) are orthogonal: (14) = 0. (x) M Figure 1 c) Assume a particle has a wave-function y(x) sketched in Fig. 2....
The expression Φ(x, h)-(1-2xh + h2)-1/2 where |hl < 1 is the generating function for Legendre polynomials. φ(x, h) can be expressed as a sum of Legendre polynomials The function (x, h) = Po(x) + h...
The expression Φ(x, h)-(1-2xh + h2)-1/2 where |hl < 1 is the generating function for Legendre polynomials. φ(x, h) can be expressed as a sum of Legendre polynomials The function (x, h) = Po(x) + hA(x) + h2Pg(x) + hn (x) The generating function of the Legendre polynomials has some applications in Physics, such as expressing the electric potential at point P due to a charge q. The location of the charge is r with respect to the origin O...
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...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
Problem #1 ---- -15pts- vvhat is the physical sense of the quantity Do in the expression for the wave-function *(x) = $(x) exp(':) (x) is real? where the function
PRINT YOUR NAME (on every page) Midterm exam 32300 G-Introduction to Quantum Mechanics-Prof. Krusin Solve all 4 problems 15pts Problem #1 What is the physical sense of the quantity po in the expression for the wave-function: Cx) (x) exp ( ipox where the function (x) is real? 25ntc
Write the expression for y as a function of x and t for a sinusoidal wave along a rope in the negative x direction with the following characteristics: A = 8.00 cm: lambda = 80.0 cm: f= 3.00 Hz and y(0, t) = 0 at t = 0. Write the expression for y as a function of x and t for the wave in part (a) assuming y(x, 0) = 0 at x = 10.0 cm.
Problem 2.6 Although the overall phase constant of the wave function is of no physical significance (it cancels out whenever you calculate a measurable quantity), the relative phase of the coefficients in Equation 2.17 does matter. For example, suppose we change the relative phase of ψι and in Problem 2.5: where ф įs some constant. Find ų,(x,t), Ux.t)12, and (x), and compare your results with what you got before. Study the special cases φ = π/2 and φ = π....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively. Derive the expression for the inner product (4) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? b) Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states [4) and (o) are orthogonal: (14) = 0. (x) M Figure 1 c) Assume a particle has a wave-function y(x) sketched in Fig. 2....
The expression Φ(x, h)-(1-2xh + h2)-1/2 where |hl < 1 is the generating function for Legendre polynomials. φ(x, h) can be expressed as a sum of Legendre polynomials The function (x, h) = Po(x) + hA(x) + h2Pg(x) + hn (x) The generating function of the Legendre polynomials has some applications in Physics, such as expressing the electric potential at point P due to a charge q. The location of the charge is r with respect to the origin O...
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...
3. Consider the wave function (x, t) = Ae-2 -ut Where A, 2, and are positive real constants. (a) Normalize Y. (b) Determine the expectation values of x and x?. (c) Find the standard deviation of x. Sketch the graph of V', as a function of x, and mark the points (x) + a) and (x) -o to illustrate the sense in which represents the spread" in x. What is the probability that the particle would be found outside this...
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