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d) and e) please
Consider an electron subjected to the potential of a one-dimensional harmonic oscillator. In addition, it is also subjected to the action of a uniform electric field of value = 6,5x106 volts/m in the direction of oscillation. The state of the system at time t = 0 is given as: (x,0) = 240(x) + 3i4₁(x) +43(x), where on are the components of the eigenvectors of the system in the representation. The frequency of harmonic oscillation is w = 1,50x10¹3 Hz. a) What values of the energy can be found and with what probabilities at instant t = 0? b) Find the mean value of the position, linear momentum and energy at time t = 0. c) If a measurement is made and the particle is found to be in its first excited state, write the state of the system immediately after the measurement. If the particle is an electron, determine the probability of finding the particle between the equilibrium position and infinity after the measurement. d) Write the time evolution of the system after measurement.
e) Assuming that the energy of the electron is the mean value H in the given quantum state, (0)), determine the probability of finding to the particle beyond the classical limit for any instant of time.