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- 2. A three-state system has energy eigenfunctions $1(x), Þ2(x) and $3(x) with corresponding energy eigenvalues -ħw, 0, ħw respectively. The system is in the initial state of wavefunction p(x, 0) = c1 $1(x) + c2$2(x) + 2c2¢2(x) where w, C1, C2 are positive real constants. If the expectation value of the Hamiltonian in this state is equal to -0.64hw a. Obtain c1 and c2 b. Write the normalized wavefunction (x, t) c. Determine the uncertainty in energy AE in the state of wavefunction (x, t) d. What is the probability of measuring the energy ħw at time t?Still think that unit conversion isn't important? Here is a widely publicized, true story about how failing to convert units resulted in a huge loss. In 1998, the Mars Climate Orbiter probe crashed into the surface of Mars, instead of entering orbit. The resulting inguiry revealed that NASA navigators had been making minor course corrections in SI units, whereas the software written by the probe's makers implicitly used British units. In the United States, most scientists use Sl units, whereas most engineers use the British, or Imperial, system of units. (Interestingly, British units are not used in Britain.) For these two groups to be able to communicate to one another, unit conversions are necessary. The unit of force in the SI system is the newton (N), which is defined in terms of basic Sl units as 1 N=1 kg · m/s?. The unit of force in the British system is the pound (lb), which is defined in terms of the slug (British unit of mass), foot (ft), and second (s) as 1 lb =1 slug ·…B3
- 3. A system of N harmonic oscillators of frequency w are prepared in identical initial states of wavefunction Þ(x,0). It is found that the measurement of the energy of the system at t = 0 gives 0.5hw with probability 0.25, 1.5hw with probability 0.5 and 2.5hw with probability 0.25. a. Write a possible function p(x, 0). b. Write the corresponding (x, t). c. What is the expectation value of the Hamiltonian in the state p(x,t) ? d. Calculate the expectation value of position at time tI need the answer as soon as possibleQ10 What is the significance of the wave function?
- 1Answer all these questionsQ2: ITX The wavefunction for the system is y (x) = A sin for 0C/ Calculate the probability of a particle in one dimensional wave function ((x)= (2/a)¹/² sin (nrx/a)) and wave long the interval (a/4 < x < 3a/4)500 neutrons freely moving inside box his walls is x=0 and x=L, if the wavefunction of every neutron at time 0 is p(x) = Ax(L + x²) a- find the normalization constant A b- calculate the average of the kinetic energy (T) of each neutron in range 0Recommended textbooks for youCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
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