An exact measurement of the position of a Simple Harmonic Oscillator (SHO) is made with the result x = x0, [The SHO has energy levels En (n = 0, 1, 2, . . .) and associated normalized wave functions $${\psi _{\text{n}}}$$ ]. Subsequently, an exact measurement of energy E is made, using the general notation Pr(E = E') denoting the probability that a result E' is obtained for this measurement, the following statements are written. Which one of the following statements is correct?
A. Pr(E = E0) = 0
B. Pr(E = En) = 1, for some value of n
C. Pr(E = En) $$ \propto {\psi _{\text{n}}}\left( x \right)$$
D. Pr(E > E'') > 0, for any E''
Answer: Option A
A. In the ground state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half
B. In the first excited state, the probability of finding the particle in the interval $$\left( {\frac{L}{4},\,\frac{{3L}}{4}} \right)$$ is half This also holds for states with n = 4, 6, 8, . . . .
C. For an arbitrary state $$\left| \psi \right\rangle ,$$ the probability of finding the particle in the left half of the well is half
D. In the ground state, the particle has a definite momentum
A. (e-ax1 - e-ax2)
B. a(e-ax1 - e-ax2)
C. e-ax2 (e-ax1 - e-ax2)
D. e-ax2 (e-ax1 - e-ax2)
A. 0.75
B. 0.50
C. 0.35
D. 0.25
Join The Discussion