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Consider a 1-dimensional quantum system of one particle Question 01: in which the particle is under a potential V(x) = ;mw?x?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region -0 < x < o. • What is the averaged position at which the particle may be found while it is in the ground state? • What is the uncertainty in the position in the ground state? • What is the uncertainty in the momentum in the ground state?

Consider a 1-dimensional quantum system of one particle Question 01: in which the particle is under a potential V(x) = ;mw?x?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region -0 < x < o. • What is the averaged position at which the particle may be found while it is in the ground state? • What is the uncertainty in the position in the ground state? • What is the uncertainty in the momentum in the ground state?

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Question 01: in which the particle is under a potential V(x) = mw?x?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region Consider a 1-dimensional quantum system of one particle -0 < x < o. • What is the averaged position at which the particle may be found while it is in the ground state? What is the uncertainty in the position in the ground state? • What is the uncertainty in the momentum in the ground state? • See if Heisenberg uncertainty principle is varified at the ground state? • Calculate the probability that the particle make a transition to the first excited state under the operator O = q. • Varify that the lowest two states of the system are mutually orthonormal.
Transcribed Image Text:Question 01: in which the particle is under a potential V(x) = mw?x?, with m being the mass of the particle and w being a parameter (you may take it as angular fre- quency) with inverse dimension of time. The particle may be found in the region Consider a 1-dimensional quantum system of one particle -0 < x < o. • What is the averaged position at which the particle may be found while it is in the ground state? What is the uncertainty in the position in the ground state? • What is the uncertainty in the momentum in the ground state? • See if Heisenberg uncertainty principle is varified at the ground state? • Calculate the probability that the particle make a transition to the first excited state under the operator O = q. • Varify that the lowest two states of the system are mutually orthonormal.
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