If the potential V(x) for a one-dimensional system is independent of time, show that the expectation value for x is independent of time.

Q: The wave function of a particle is psi(x)=Ae-bx for x>0 and psi(x)=Aebx for x<0. Find the…

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Q: What is y(x) (i.e., y as a function of x) given that dy dx where you are given the boundary…

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Q: Is the function 1/r a legitimate velocity potential in planepolar coordinates? If so, what is the…

A: A velocity potential function (V) is considered to be legitimate if its Laplacian is zero. Laplacian…

Q: Find the Z Transform for the following function: f(t)=e^(-ct) cos⁡(2πt/3)u(t)

A: To find the Z-transform of the given function, we can first write the function in terms of the…

Q: The spherical symmetric potential in which a particle is moving is V (r)= ßr', where B is a positive…

A: Given, Vr=βr5 From the virial theorem, if potential energy is directly proportional to rn, then…

Q: c): A particle of mass m moves in a three-dimensional box of sides a, b, c. If the potential is zero…

A: Given a particle of mass in a three dimensional infinite depth box of sides a, b and c, where…

Q: What does your result for the potential energy U(x=+L) become in the limit a→0?

A: We want to calculate lima→0qQ8πε0alnL+aL-a=qQ8πε0lima→0lnL+aL-aa

Q: A particle of mass m moves inside a potential energy landscape U (2) = X|2| along the z axis. Part…

A: To determine the units of the constant λ, we can use the given formula for potential energy U(z) and…

Q: A particle with mass m is moving along the x-axis in a potential given by the potential energy…

A: The potential energy function U(x)=0.5mω2x2 describes a simple harmonic oscillator in quantum…

Q: This question has to do with binary star systems, where 'i' is the angle of inclination of the…

A: For a binary star system, the ratio of their velocities and their masses are related as,

Q: A particle of mass m moves in the one-dimensional potential U(x) = U, Se-x/a Sketch U(x). Identify…

A: Here, we use the maxima/minima conditions to get the required.

Q: The probability of finding particle between x and x+d 1.f Y (x, t) = 1 80 2. p(x,t) = 1 3. Y (x,…

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Q: Evaluate the following expectation values: (a) ⟨ℓ,m1​∣Lx​∣ℓ,m2​⟩ (b) ⟨ℓ,m1​∣Ly​∣ℓ,m2​⟩

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Q: Question 1: Determine the bandwidth ( waw ) and sampling time interval for the following…

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Q: Prove that the expression e*/(1+ e*)² is an even function of x.

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Q: Evaluate the (a) reflection amplitude, and the (b) reflection probability of a step potential x > a…

A: Given: The step potential of the barrier is given as V(x) = V02;    x > a-V02; x ≤ a The energy…

Q: How would I be able to sketch the graph in problem 7.36?

A: (a) The potential energy U as a function of x is

Q: 2. f= (2y + + x j +3yz %3D

A: Given, F=2xy+z3i→+x2j→+3yz2k→∇×F=i^j^k^∂ ∂x∂ ∂y∂ ∂z2xy+z3x23yz2Solving we get=∂ ∂y3yz2-∂ ∂zx2i^-∂…

Q: Assuming a perfectly inelastic collision in one dimension, apply the principle of conservation of…

A: Introduction: Perfectly inelastic collision: In it, two objects collide to form one big mass system…

Q: We have a free particle in one dimension at a time t 0, the initial wave function is V(x,0) =…

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Q: tropy H(X | Y ) in terms of the joint distribution and associated conditional probabilit

A: Let us consider p(x, y) to be the joint probability distribution of the two random variables X and Y…

Q: (Vax + b - 4 f(x) = x #0 3, x = 0 Determine the values of the real numbers a and b so that f(x) is…

A: Given,

Q: If a wavefunction is normalized at time t=0, show that it remains normalized at all times.

A: Consider a wavefunction is normalized at time t = 0The condition for normalization at t = 0 is…

Q: A particle experiences a potential energy given by U(x) = (x². - 3)e-x² (in Sl units). (a) Make a…

A: b) For the particle to remain bound, it must have an energy less than zero since the potential…

Q: A particle is described by the following function: A Y = , for 1 < x < 4 (x+1)(x²+9)²' a. Find the…

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Q: Consider a potential barrier represented as follows:  U(x) = 0 if x a  Determine the transmission…

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Q: Suppose that an input of x(t) is applied to a causal LTI system whose magnitude response and phase…

A: Given that,Input = x(t)Transfer function = H(w)And,         x(t) = 2 + 2 cos8πt+2 cos(16πt) +2…