Dirac notation Definition and 103 Threads

Hi everyone, my problem is this Using Dirac notation show that \frac{d}{dt}<\varphi|\hat{A}|\varphi> = \frac{i}{\hbar}<\varphi|[\hat{H},\hat{A}]|\varphi> where A does not explicitly depend on t I am given as a hint that the hamiltonian operator in Dirac notation is...

1.) an inner product of a state vector represent by <\psi|\psi>. sometimes the notation is like <\phi|\psi> is mean transfer from state |\psi> to <\phi|.it mean the former 1 do not transfer the state? what is the difference between both? 2.) what is mean by <x|\psi>? is it mean x(position)...

Homework Statement 1. Given that |ψ> = eiπ/5|a> + eiπ/4|b>, express <ψ| as a linear combination of <a| and <b|. 2. What properties characterise the bra <a| that is associated with the ket |a>? Homework Equations The Attempt at a Solution 1. <ψ| = e-iπ/5<a| + e-iπ/4<b| 2. a. The bra <a|...

Hello, I'm in an introductory course about quantum computing. My math experience is fairly solid, but not very familiar with Dirac (bra-ket) notation. Just would like to clarify one thing: In a single cubit space, we have |0 \rangle , and | 1 \rangle . I understand that these form an...

Alright... So I'm in an 'introductory' Q.M class in college right now, it's the only one that this two-year college has, so I don't have an upper division Q.M Profs to talk to about this, and since my prof is equally confused, I turn to the internet. Okay, so everyone knows that <ψ|Aψ> = <a>...

Homework Statement Imagine you have two vectors |a> and |b> such that: |c> = |a> + |b> Now imagine you want the dot product: <c|a> Is that the same as: <c|a> = [ <a|*+<b|* ] |a> = <a*|a> + <b*|a> where * represents the complex conjugate of the vector? Homework Equations...

How would you simplify this expression: <a|<b|a>|a> where ψ = |a>|b> and I'm finding ψ*ψ.

Hi all! If you are given an operator such that A|1> = √(1/3) |1> +√(2/3) |2>, how do we interpret it? I do know that 1/3 and 2/3 are probabilities but is this operator application on state one suggesting that this state in state 1 and 2 with probabilities 1/3 and /3 respectively? Thank you!

Can anyone point me to how to interpret Dirac notation expressions as wave functions and integrals beyond the basics of     <α| = a*(q)     |β> = b(q)     <α|β> = ∫ a* b dq For example in the abstract Dirac notation the expression     |ɣ> (<α|β>) can be evaluated as     (|ɣ><α|) |β>  ...

Square integrable functions -- Hilbert space and light on Dirac Notation I started off with Zettilis Quantum Mechanics ... after being half way through D.Griffiths ... Now Zettilis precisely defines what a Hibert space is and it includes the Cauchy sequence and convergence of the same ... is...

I'm having trouble seeing how an operator can be written in matrix representation. In Sakurai, for an operator X, we have: X = \sum \sum |a''> <a''| X |a'> <a'| since of course \sum |a> <a| is equal to one. Somehow, this all gets multiplied out and you get a square matrix with the...

In Sakurai's Modern Quantum Mechanics, he develops the Dirac notation of bras and kets. In one part, he states (page 17): <B|X|A> = (<A|X^|B>)* = <A|X^|B>* where X^ denotes the Hermitian adjoint (the conjugate transpose) of the operator X. My question is, since a bra is the conjugate...

\{\vec{A},\vec{B}\}\cdot \vec{C}=\vec{A}(\vec{B}\cdot \vec{C}) \vec{C} \cdot \{\vec{A},\vec{B}\}=(\vec{C}\cdot \vec{A}) \vec{B} I want to write dyade in Dirac notation. (|\vec{A}\rangle\langle\vec{B}|)|\vec{C}\rangle= |\vec{A}\rangle\langle\vec{B}|\vec{C}\rangle...

Homework Statement Find <P>. P = i√(mhw/2)(a†-a). Note a† and a are the ladder operators. P is the momentum operator of the harmonic oscillator. |ψ > = (1/sqrt(2))[ |1> - i |2>] The answer should be zero, can someone check my work?Homework Equations a† |n> = sqrt(n+1)|n+1> a |n> =...

Homework Statement [A^{+}A]=1 A|a>=\sqrt{a}|a-1> A^{+}|a>=\sqrt{a+1}|a+1> <a'|a>=\delta_{a'}_{a} Homework Equations what is 1 <a|A|a+1> 4. <a+1|A^{+}|a> 3. <a|A^{+}A|a> 4. <a|AA^{+}|a> The Attempt at a Solution 1. <a|A|a+1> =<a|\sqrt{a+1}|a+1-1>=\sqrt{a+1}<a|a> since a=a and...

Homework Statement http://img857.imageshack.us/img857/2079/dirac.png Homework Equations H|ψ> = E|ψ> L^{2}|ψ> = l(l+1)\hbar^{2}|ψ> L_{z}|ψ> = m_{l}\hbar|ψ> The Attempt at a Solution I know this problem is very simple since I've seen a very similar problem a while ago but I've completed forgot...

Homework Statement Find <lz> using \Psi, where \Psi=(Y11+cY1-1)/(1+c^2)). Ylm are spherical harmonics, and <lz> is the angular momentum operator in the z direction. Homework Equations <lz> Ylm = hmYlm The Attempt at a Solution The brackets around <lz> are throwing me off...

Alright, so I was wondering if anyone could help me figure out from one step to the next... So we have defined |qt>=exp(iHt/\hbar)|q> and we divide some interval up into pieces of duration τ Then we consider <q_{j+1}t_{j+1}|q_{j}t_{j}> =<q_{j+1}|e-iHτ/\hbar|q_{j}>...

Homework Statement http://quantum.leeds.ac.uk/~almut/section2.pdf Please note i am referring to the above notes I basically don't get how the maths works to get (eq(25))(eq(22))(eq(24)) = eq(26) am i missing something interms of the commutator relations ? Homework Equations The Attempt at a...

I am new to quantum physics. My question is how to write the Hamiltonian in dirac notation for 3 different states say a , b , c having same energy. I started with Eigenvaluee problem H|Psi> = E|psi> H = ? for state a? SO it means that indvdually H= E (|a><a|) for state a and for all three...

Homework Statement For the infinite square well, a particle is in a state given by \psi = \frac{1}{\sqrt 2}(\psi_1 + \psi_3) , where \psi_1 and \psi_3 are energy eigenstates (ground state and the second excited state, respectively). Represent this state as a column matrix \psi> in...

Homework Statement I have the state: |\psi>=cos(\theta)|0>+sin(\theta)|1> where \theta is an arbitrary real number and |\psi> is normalized. And |0> and |1> refer to the ground state and first excited state of the harmonic oscillator. Calculate the expectation value of the Hamiltonian...

Hi all, I was diving into my 3rd year quantum assignment and I saw the following which I have to use for the rest of the question to prove the Cauchy-Schwarz inequality: Homework Statement || a|x> + b|y> ||^2 I only really learned a bit about Dirac notation last year, so please...

Homework Statement Normalised energy eigenfunction for ground state of a harmonic oscillator in one dimension is: 〈x|n〉=α^(1/2)/π^(1/4) exp(-□(1/2) α^2 x^2) n = 0 α^2=mω/h suppose now that the oscillator is prepared in the state: 〈x|ψ〉=σ^(1/2)/π^(1/4) exp(-(1/2) σ^2 x^2)...

Homework Statement Show that \left\langlex|p|x'\right\rangle = \hbar/i \partial/\partialx \delta(x-x') 2. The attempt at a solution \left\langlex|p|x'\right\rangle = i\hbar \delta(x-x')/(x-x') = i\hbar \partial/\partialx' \delta(x-x') = \hbar/i \partial/\partialx \delta(x-x') For...

I am confused about two minor things right now. The following illustrates both which I pulled from my QM book: <x|p_{op}|0>=\int_{-\infty}^{\infty}dp<x|p_{op}|p><p|0>=\int_{-\infty}^{\infty}dp~p<x|p><p|0>...

Homework Statement Suppose we have a spin 1/2 Particle in a prepared state: \left|\Psi\right\rangle = \alpha \left|\uparrow\right\rangle + \beta\left|\downarrow\right\rangle where \left|\uparrow\right\rangle \left|\downarrow\right\rangle are orthonormal staes representing spin up and...

sorry if this looks ugly but I couldn't find out how to write out bras and kets on the Latex thing. I have these inner products <f|g> = i<x|(AB - A<B> - <A>B + <A><B>)|x> and <g|f> = -i<x|(BA - B<A> - <B>A + <A><B>)|x> where |x> is some arbitrary ket and A and B do not commute. I'm trying to...

Homework Statement Please see attached Homework Equations The Attempt at a Solution Ok so basically a bit confused about notation.. does |psi> = sum over all r of ar |ur> ? any help would be great..thanks

Homework Statement Please see attached :) Homework Equations The Attempt at a Solution Hmm ok so stuck on all parts really..starting with (a), i see that we are looking for the probability that it is in state Eroot6 i.e. |root6> but how do we work this out? It's not a state...

Homework Statement Hi guys Ok, I have some questions, which I would very much like for you guys to help me with. Say I have some state |1>, which denotes the first, n=1, solution of the infinite, square well. |1> is a vector in the Hilbert space spanned by all the eigenvectors of the...

Homework Statement trying to simplify (using dirac notation) QM: <E| (QH - HQ) |E> using H|E> = E|E> Homework Equations The Attempt at a Solution the textbook says that it simplifies to (E-E) <E|Q|E> = 0 but i can't see how :S

Say we have, |\chi_3>=|a+ib> and we want : <\chi_3|H|\chi_3> is it correct to say: <\chi_3|H|\chi_3>= <a|H|a>+<a|H|ib>+<-ib|H|a>+<-ib|H|ib> ??

Hi, I find a lot of the time in QM i have been calculating things blindly. Take the expectation value for instance. I have worked this out in integral form plenty of times, but haven't really understood why I'm doing what I'm doing. I looked up wikipedia and apparently, for a measurable...

Hi, I'm desperately searching for some literature which discusses the harmonic oscillator, preferably simple, in terms of the path integral formulation. I am unfamiliar with dirac notation and want something as simple as possible which gives general results of the harmonic oscillator in terms of...

Expectation value of operator A is given by following formula in Dirac notation. <A> = <x|A|x> where A : Operator <A> : Expectation value of A |x> : State Somehow I am unable to convince myself that this formula is true. Would someone please explain it to me? Thanks

I was reading some more quantum mathematics, and a question occurred to me. In the current treatment of the topic, the bra-ket notation is defined as a shorthand notation for more complex mathematical operations. But couldn't bra-ket notation be defined separately from quantum physics? In other...

Homework Statement my apologies if this question should be posted in the math forum 3-d space spanned by orthonormal basis: (kets) |1>, |2>, |3>. Ket |a> = i|1> - 2|2> - i|3>. Ket |b> = i|1> + 2|3>. The question is to construct <a| and <b| in terms of the dual basis (kets 1,2,3)...

Hi everybody, I am trying to get the partial derivative of the following with respect to Si[t] and Phi[t] separately: Integrate[<Phi[t]|H|Si[t]>] The operator H is the partial derivative with respect to t. I tried this in Mathematica, calling Needs["Quantum`Notation`"] but I...

Hello, I'm fuzzy on how Dirac notation works especially when operators are added in. Does anyone have a clear explanation (the simpler the better) that they can give to me, and or a website or book that does a good job of explaining it?

I am working through a problem relating to the conservation of probability in a continuity equation. However, I end up with a contradiction when trying to put the following into the Time-Dependent Schrodinger Equation \frac{\partial\psi(x)}{\partial t}=\frac{\partial\left\langle...

Homework Statement I'm given the eigenvalue equations L^{2}|\ell,m> = h^2\ell(\ell + 1)|\ell,m> L_z|\ell,m> = m|\ell L_{\stackrel{+}{-}}|\ell,m> = h\sqrt{(\ell \stackrel{-}{+} m)(\ell \stackrel{+}{-} m + 1)}|\ell, m \stackrel{+}{-} 1> Compute <L_{x}>. Homework Equations Know...

I have recently finished reading a section on this notation, and while i though i understood it, i now find myself lost The question is to show that <m|x|n> Is zero unless m = n + or - 1 As I understand it so far <m| and |n> correspond to the eigenstates of an arbitrary system and x...

Hi. I came across a problem in a book of mine that requires me to find the dual of a vector |x> = A |a> + B |b>. However, it's a bit sketchy about taking |x> to <x|. With a little algebra, I got |x>i = A |a>i + B |b>i So <x|i = |x>i* = (A |a>i + B |b>i)* = (A |a>i)* + (B |b>i)* = A*...

Hey guys, I am having difficulty interpreting M(x,x') into dirac notation. How do i write M(x,x') in dirac notation? The actual problem is to write the following in dirac notation: int { int { m(x)* M(x,x') g(x') } dx} dx' I would appreciate your help.

Defining the state | \alpha > such that: | \alpha > = Ce^{\alpha {\hat{a}}^{\dagger}} | 0 >\ ,\ C \in \mathbf{R};\ \alpha \in \mathbf{C}; Now, | \alpha > is an eigenstate of the lowering operator \hat{a}, isn't it? In other words, the statement that \hat{a} | \alpha >\ =\ \alpha | \alpha >...

A professor of mine recently remarked that dirac notation is easily the best in physics & we'd quickly realize this once we take a course in relativity. I've already taken the course & I find myself disagreeing with him, but maybe that's only because I enjoy relativity more. Curious what you...

Hi all, I recently purchased Shankar's Principles of Quantum Mechanics which relies heavily on Dirac's bra-ket notation. I'm just wondering if this is the norm or should I get used to switching between what I'm learning and some other accepted standard notation? Thanks in advance!

Consider the following state vector and Hamiltonian: |\psi (0) \rangle = \frac{1}{5}\left (\begin{array}{cc}3\\0\\4\end{array}\right ) \hat{H} = \left (\begin{array}{ccc}3&0&0\\0&0&5\\0&5&0\end{array}\right ) If we measure energy, what values can we obtain and with what probabilities...

Consider a particle in a harmonic pscillator potential V (x) is given by V = \frac{1}{2}m\omega^2 Also \hat a = n^\frac{1}{2}|n-1>, and \hat a\dagger = (n-1)^\frac{1}{2}|n-1> where \hat a = \frac{\beta}{\sqrt 2}(\hat x + \frac{i\hat p}{m\omega}) \hat a\dagger =...