A one-dimensional harmonic oscillator is in the state $$\psi \left( x \right) = \frac{1}{{\sqrt {14} }}\left[ {3{\psi _0}\left( x \right) - 2{\psi _1}\left( x \right) + {\psi _2}\left( x \right)} \right],$$ where, $${\psi _0}\left( x \right),\,{\psi _1}\left( x \right)$$ and $${\psi _2}\left( x \right)$$ are the ground, first excited and second excited states, respectively. The probability of finding the oscillator in the ground state is
A. zero
B. $$\frac{3}{{\sqrt {14} }}$$
C. $$\frac{9}{{14}}$$
D. 1
Answer: Option C
Related Questions on Quantum Mechanics
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
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