A quantum oscillator consists of a particle and a weightless spring. The particle has the molar mass 0.500 g/mol and the force constant of the spring is 510 N/m. The equilibrium length of the spring Lois 74 pm, but we may not use this number because all of the following questions are based on the displacement x = L-Lo) where L is the instantaneous bond length). (a) (15 pt) Determine a and the position of the two turning points for the one-dimensional quantum oscillator with v = 5. (b) (10 pt) Write the wave function Wyns (x) (as a function of x, not y). Determine the value of the normalization constant and its unit. (c) (10 pt) Find the probability density distribution ves at the turning point.