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?
Dirac notation, also known as bra-ket notation, is a mathematical notation used to represent quantum states and operations in quantum mechanics. It was introduced by physicist Paul Dirac in the 1930s and has become an essential tool in the study of quantum mechanics.
Dirac notation uses a combination of angled brackets, or "bras" and "kets," to represent vectors and operators in quantum mechanics. These symbols are not used in traditional mathematical notation, where vectors are typically represented by boldface letters or arrows.
The "bra" and "ket" symbols represent two different types of vectors in quantum mechanics. The "bra" vector, denoted by <a|, represents a row vector, while the "ket" vector, denoted by |b>, represents a column vector. Together, they form an inner product <a|b>, which is used to calculate the probability of transitioning from one quantum state to another.
Dirac notation is used to represent quantum states, operators, and measurements in a concise and elegant manner. It allows for the easy manipulation and calculation of complex quantum systems, making it an essential tool in the study of quantum mechanics. It is also used in the development of quantum algorithms and in the analysis of quantum information.
No, Dirac notation is not the only way to represent quantum states and operations. Other common notations include matrix representation, state vector representation, and wave function representation. However, Dirac notation is widely used and preferred by many physicists and mathematicians due to its simplicity and versatility.