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) A particle of mass m and energy E moving along the x axis is subjected to a potential energy function U(x).
\((25\) marks) A particle of mass \(m\) and energy \(E\) moving along the \(x\) axis is subjected to a potential energy function \(U(x) .\) (a) Suppose \(\psi_{1}(x)\) and \(\psi_{2}(\mathrm{x})\) are two wave functions of the system with the same energy \(E .\) Derive an expression to relate \(\psi_{1}(x), \psi_{2}(x)\), and their derivatives. (b) By requiring the wave functions to vanish at infinity, show that \(\psi_{1}(x)\) and \(\psi_{2}(x)\) can at most differ by a multiplicative constant. Hence, what conclusion can you...
A particle of mass m is constrained to move along the x-axis and is subjected to a force given by . Assuming the particle had an initial velocity of Vo and was at the origin at t = 0, find an equation for the particle's velocity and set up the integral from which the position equation as a function of time could be determined. NOTE: You do not need to evaluate the integral for the position as a function of...
Potential Energy and Force A mass m=3.00kg moving along the x-axis is acted on only by a single conservative force. The force has a potential energy function given by U(x)=(1.00J/m3)x3−(9.00J/m2)x2+(15.0J/m)x. It will be useful to graph this function on your calculator or computer. Part A Find the force on the mass as a function of x. (Leave the units out of the coefficients in your expression, and make sure all coefficients have three significant figures). F(x) = N SubmitMy AnswersGive...
A particle of mass m = 2.70 kg moving along the x axis from x = 0 to x = 10.6 m experiences a net conservative force in an isolated system given by F = 5x − 4, where F is in newtons and x is in meters. (a) What is the work done on the particle by the force F? J (b) What is the change in the potential energy of the system during this motion? J (c) If...
A particle of mass 1.80 kg moves along the x-axis with a potential energy whose dependence on x is shown in the figure. The particle has speed 4.714 m/s at x=12.0 m. What are the minimum and maximum x-position the particle can have? U(x)(J) 12.0 8.0 4.0 0 16.0 8.0 20.0 x(m) 4.0 12.0 -4.0 -8.0 -12.0
24&25 please The figure below shows the potential energy function U (r)for a particle moving along an axis labeled by the coordinate r. Values for energy and distance are in joules (j) millimeters (mm), respectively. The total energy of this particle is E = -4 J. Initially, the particle is at r = 1 mm and moving to the right (direction of increasing r) Which of the following statements best describes the subsequent motion of this particle? a. The particle...
Question #9 all parts thanks 9. The wavefunction, p(x,t), of a particle moving along the x-axis, whose potential energy V(x) is independent of time, is described by the one-dimensional non-relativistic Schrödinger equation (where m is its mass, h is the reduced Planck constant, i is the imaginary number): 2m (a) Verify that it is a parabolic equation (page E-1-2). [It has wave-like solutions, however.] (b) Use the substitution Px,t)-Xx)Tt) to separate the equation into two ODEs. (c) Solve for T,...
The position function x(t) of a particle moving along an x axis is x = 5.00 - 6.00t2, with x in meters and t in seconds. (a) At what time and (b) where does the particle (momentarily) stop? At what (c) negative time and (d) positive time does the particle pass through the origin?