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In the dirac notation for a quantum state of a system, an eigenstate wave function un is replaced by the vector |n>, and a general state wave function ψ by |ψ>.
a) Translate the following mathematical statements to the corresponding forms n wave mechanics: i) <n|m> = δnm, and ii) <n|A|m> = (<m|A|n>)*, where A is an hermitian operator.
b) By considering the expansion of |ψ> in terms of |n>, derive the following result which expresses the completeness property of the set of eigenstates.
∑|n><n|= 1.
A 68.8 kg ice skater is skating along in a straight line (in the positive direction) at 8.8 m/s when he bends down and scoops up his 24.4 kg doggy sitting still on the ice. What will be the new velocity of the dog-n-skater?
The length of a string is 322 cm. It is held fixed at each end. The string vibrates in seven sections; such as the string has seven antinodes, and the string vibrates at 160 Hz.
Q.A uniform ladder of length '2L'and mass 'm' leans against a wall in a vertical plane at an angle 'θ' to the horizontal. The floor is rough, having a coefficient of static friction 'µ'. A person of mass 'M' stands on the ladder at a distance 'D' fro..
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express what would be the frequency of vibrations.
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