The discussion revolves around quantum mechanics, specifically focusing on Dirac notation and the interpretation of quantum states and probabilities. Participants are exploring various aspects of a problem related to measuring quantum states and calculating probabilities associated with those states.
Some participants have provided guidance on calculating probabilities and interpreting quantum states, while others are seeking clarification on specific concepts and calculations. Multiple interpretations of the problem are being explored, particularly regarding the stability of quantum states post-measurement.
Participants are navigating foundational concepts in quantum mechanics, with some expressing uncertainty due to their early stage in learning the subject. There are references to textbook resources and exam preparations, indicating a broader context of academic pressure and learning challenges.
JesseC said:If you were to measure what state particle was in, you'd find it in one of those states, not a mixture. The probability of finding it in one of the states is given by the coefficient of the state squared.
Root 6 is about 2.5. So the question is asking you what the probability is of finding the particle in a state less than 2.5. What is the probability of finding the particle in either the n=1 or n=2 state?
bon said:oh i see okay thanks. So is it 0.2^2 + 0.3^2? i.e. P(finding it in state 1) + P(finding it in state 2)?
What is H|ψ> equal to?bon said:Thanks okay! I'm now trying to do (b),(c),(d)
(b) : To work out mean value of energy i know i just work out the sum of En P(En) over all energies right? But how do i derive this from just the knowledge that the mean value of energy is <psi|H|psi> ?
Can you think of a reason that they should not stay the same?(c): So i know i just multiply every state by e^-iEn/h t Do (a) and (b) stay the same?
What is the wavefunction of the system after the measurement? If you understand part (a) and given that wavefunction, what is the probability that the system will be found in states |1>, |2> and |3>?(d): The system is in state |4> and it will stay in this state? Is this right??
kuruman said:Can you think of a reason that they should not stay the same?
kuruman said:What is the wavefunction of the system after the measurement? If you understand part (a) and given that wavefunction, what is the probability that the system will be found in states |1>, |2> and |3>?
You guess right.bon said:No i guess they are the same then?
It will unless you perturb it. Note that you can write this state as 0*|1>+0*|2>+0*|3>+1*|4>.Well after the measurement the state of the system is surely |4>. Won't it stay there?