A particle in a harmonic oscillator potential with spring constant is known to be in a superposition of two energy eigenstates in which it is four times as likely to be found with energy as it is to be found with energy (a) Write down a properly normalized state function using harmonic oscillator energy eigenstates that has the above statistical property. (b) Calculate the energy expectation value for this state. (c) Calculate the expectation values for this state. (d) Use the result of part (c) to find the position-momentum uncertainty product for this state. Hint: This problem can best be solved using creation and annihilation operators. If you do that you will not have to do any actual integrations to calculate the expectation values.