A quantum system described by a Hamiltonian H is in the state √√√√/101) - 1/21(02) + √/15 ( Φ1) (1 + 21) (03) + √5164)], |y) = N where lon) are the eigenstates of energy such that Ĥ|¢n) = nEo|¢n), Eo has units of energy, and NER. (c) What is the expectation value of the energy when the system is in the state |⁄)? Is it a possible measurement result if the energy is measured? (d) Consider an operator Â, the action of which on |øn) (n = 1, 2, 3, 4) is defined by X|øn) = (n + 5)xo|n), where xo is a real-valued scalar. Suppose that a measurement of the energy of the above-defined |⁄) yields 3£º. Assume that immediately afterwards, we ideally measure the physical quantity correspond- ing to X. What is the value for the quantity obtained in the latter measurement?
A quantum system described by a Hamiltonian H is in the state √√√√/101) - 1/21(02) + √/15 ( Φ1) (1 + 21) (03) + √5164)], |y) = N where lon) are the eigenstates of energy such that Ĥ|¢n) = nEo|¢n), Eo has units of energy, and NER. (c) What is the expectation value of the energy when the system is in the state |⁄)? Is it a possible measurement result if the energy is measured? (d) Consider an operator Â, the action of which on |øn) (n = 1, 2, 3, 4) is defined by X|øn) = (n + 5)xo|n), where xo is a real-valued scalar. Suppose that a measurement of the energy of the above-defined |⁄) yields 3£º. Assume that immediately afterwards, we ideally measure the physical quantity correspond- ing to X. What is the value for the quantity obtained in the latter measurement?
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![A quantum system described by a Hamiltonian Ĥ is in the state
1
|--1/10/17 - 15/1/2) + √√/53 (1 +21) 103) + √5101)].
|y) = N
where on) are the eigenstates of energy such that Ĥ|¢n) = nEo|ón), Eo has units of
energy, and NER.
(c) What is the expectation value of the energy when the system is in the state |√)?
Is it a possible measurement result if the energy is measured?
=
(d) Consider an operator Î, the action of which on |øn) (n = 1, 2, 3, 4) is defined
by Xon)
(n + 5)xo|on), where xo is a real-valued scalar. Suppose that a
measurement of the energy of the above-defined |ý) yields 3Eº. Assume that
immediately afterwards, we ideally measure the physical quantity correspond-
ing to X. What is the value for the quantity obtained in the latter measurement?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F466dfe05-514c-4e8d-9e28-eee295fc0d76%2F9936fd31-cc61-439c-bb69-a9f7a9c074ee%2Fnc4mf74_processed.png&w=3840&q=75)
Transcribed Image Text:A quantum system described by a Hamiltonian Ĥ is in the state
1
|--1/10/17 - 15/1/2) + √√/53 (1 +21) 103) + √5101)].
|y) = N
where on) are the eigenstates of energy such that Ĥ|¢n) = nEo|ón), Eo has units of
energy, and NER.
(c) What is the expectation value of the energy when the system is in the state |√)?
Is it a possible measurement result if the energy is measured?
=
(d) Consider an operator Î, the action of which on |øn) (n = 1, 2, 3, 4) is defined
by Xon)
(n + 5)xo|on), where xo is a real-valued scalar. Suppose that a
measurement of the energy of the above-defined |ý) yields 3Eº. Assume that
immediately afterwards, we ideally measure the physical quantity correspond-
ing to X. What is the value for the quantity obtained in the latter measurement?
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