A quantum mechanical particle with mass m is placed in a potential well with the potential energy of V(x) = 2m}? 2x2, where B is a constant with the appropriate unit. For all the questions below, your result should NOT contain w. a) Write down the normalized wavefunction for the lowest energy level that this particle can be on (i.e., nd |0)). b) Calculate the normalized wavefunction for the energy level with an energy of 5MB. 0) Check whether the two wavefunctions in parts (a) and (b) are orthogonal or not. + Drag and drop an image or PDF file or click to browse... 02 (5 points) (Continuing the question above) (1) Without using the ladder operators, calculate the expected value of momentum if the particle is in a mixed state that is expressed as g | 0) + i ll). e) Redo part ((1) using the ladder operators and the orthonormality of the energy eigenstates. You should not solve any integrals this time. Note that in order to arrive at the same result, you should include the time-dependent part of the eigenstates