For a simple harmonic oscillator determine a total energy b the kinetic energy and potential energy...
For the ground state of the 1D simple harmonic oscillator, determine the average values of the kinetic energy KE and the potential energy V and in doing so verify that (KE) = (V).
Consider the harmonic oscillator. Is it possible to measure the exact kinetic energy and exact potential energy simultaneously? Prove this mathematically.
The figure on the right shows the kinetic energy K of a simple harmonic oscillator versus its position x. (a) What is the spring constant? (b) Suppose the system consists of a block of mass 0.50 kg attached to a spring. Sketch displacement x as a function of time t. at -12 -8 -4 0 4 8 12
Question 3: A particle is in the ground state (po) of a simple harmonic oscillator potential. (a) Determine Φ(p,t). (b) Classically, the kinetic energy cannot exceed the total mechanical energy of the particle, so w. You measure the momentum of the particle. What is the probability that you will measure a value outside of the classically allowed range? 2 Reminders: foo e-a2+br dr=v/Te4a where a is real and positive. The error e edt and can be calculated numerically function is...
sider a simple harmonic oscillator with mass m and frequency ω The two lowest energy eigenstates have nd hu respectively. (a) (5 points) Calculate the expectation value of kinetic energy for the state with total energy Jhu. (b) (5 points) Calculate the expectation value of potential enerey for the state vith total enersy had
It can be shown that for a linear harmonic oscillator the expectation value of the potential energy is equal to the expectation value of the kinetic energy, and the expectation values for r and p are clearly both zeros (0) Show that in the lowest energy state Ain agreement with the uncertainty principle (b) Confirm that for the higher states (Ax)(Ap) > h/2 . Problemi 4. ( 8 pts) It can be shown that for a linear harmonic oscillator the...
Problem B: (75%) At what displacement of simple harmonic motion is the energy half kinetic and half potential? Use a spring with constant k and a mass m attached to its end as your model.
1. Consider a one-dimensional simple harmonic oscillator. We know that the total energy (E) has values: Here the angular frequency (o) corresponds to the freshman physics value of [spring constant/massja and (n) can be 0, 1,2, any non-negative integer. We know that the total energy is a measurable, observable quantity. The total energy includes the kinetic energy and the potential energy. Please explain whether or not the kinetic energy and the potential energy can both be measured at the same...
4. (20 points) Harmonic Oscillator The ground state wave function of a simple harmonic oscillator is (a) = Ae-42", where a = (a) Using the normalization condition, obtain the constant A. (b) Find (c), (), and Az, using the result of A obtained in (a). Again, A.= V(32) - (2) (c) Find (p) and Ap. For the latter, you need to evaluate (p). Hint: For a harmonic oscillator, the time-averaged kinetic energy is equal to the time-averaged potential energy, and...
[20 points] A particle in the simple harmonic oscillator potential with angular frequency a is initially in the ground state: c,y, (x) =Yo(x Att = 0 , the angular frequency of the oscillator suddenly doubles: a} → a½-2.4 The initial wave function can be written in terms of the modified potential (denoted with a tilde:~: Recall that the general form of the first few stationary states for the harmonic oscillator are given on page 56 of your text. a. What...