Questions tagged [observables]

A quantum observable is a measurable operator whose corresponding property of the state can be determined by some sequence of physical operations ("observation"), such as submitting the system to various electromagnetic fields and eventually reading a value. In systems governed by classical mechanics, any experimentally observable value can be shown to be given by a real-valued function on the set of all possible system states.

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176 views

How come there are Schrödinger Picture operators with explicit time dependence?

In the Schrödinger picture, observables are said to be time independent (see Cohen, for example) operators. However, when deriving the Heisenberg Equation of Motion $$i\hbar\frac{d}{dt}A_H(t)=[A_H(t),...
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Are eigenstates of the position operator continuous?

The way I've understood it is that eigenfunction of an operator are the different states which the actual wavefunction can take when the property/observable corresponding to the given operator is ...
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What does it mean for 2 observables to be compatible?

If I have 2 observable operators $A$ and $B$, if $A$ and $B$ commute: $[A, B] = 0$, then they must necessarily form a complete set of commuting observables (CSCO). Essentially, if 2 observables are ...
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Is a quantum gate different from taking a measurement?

I'm reading a book on quantum computing. It is a very non-technical book, and I do not need a very technical explanation. I keep on seeing the words quantum gate pop up, and I'm wondering whether this ...
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Finding measurements in non-Hermitian operators

I know how the measurement postulate in quantum mechanics works, in regard to hermitian operators, but what if an operator is non-hermitian? Can i apply the following reasoning? If an operator is ...
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140 views

Heisenberg choice of the observables and different outcomes [duplicate]

Somebody could help me to clarify how its possible that different choices of the observable to measure can lead to different outcomes of the observed system state?
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144 views

Are there any ways to exclude uncertainty in the values of any non-commuting operators? [closed]

If two similar systems are created and In the first system the position is measured with accuracy and in the second one the momentum is measured with accuracy can this avoid the uncertainty in the ...
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Does the mean value change?

We know that $x_0$ and $p_0$ are the mean values for the position and momentum of a particle in the normalized state characterized by the function $\psi (x)$, ( that is, $x_0=\langle x \rangle_\psi$ ...
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Why is there a physical preference to real numbers?

In quantum mechanics, operators can only be observables if the eigenfunctions they operate on have real eigenvalues. If they are complex, I am told that, surely, some observable of a physical system ...
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Definitions of operators and commutativity in quantum mechanics

If $[\hat A,\hat B] = 0$, where $\hat A$ and $\hat B$ are operators, then the operators commute. This also means that, when applied to a wavefunction, that one can measure observables $A$ and $B$ in ...
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Do all well-measured observables effectively commute?

Do all well-measured observables effectively commute with each other? The rest of this long post clarifies what I mean by that simple-looking question. Consider quantum field theory in Minkowski ...
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4answers
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Is there a concept of velocity at quantum level? [duplicate]

I am confused as according to Heisenberg's uncertainty principle, we cant define the position and momentum of a particle with absolute accuracy simulaneously. Then how can we define velocity at ...
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Measuring different observables simultaneously with arbitrary precision

I am trying to understand how different observables can be measured at the same time with arbitrary precision. To check if I understand it I am using an example. Let's say we have as our first ...
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If I was Schrödinger's cat, what would I feel? [closed]

What I'm doing Note before reading: I've made two edits for clarification The first starts at: "To clarify based on answers, I think ya'll are missing the meat of the question:" The second starts ...
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What happens when the same observable is measured twice in a row?

I have the understanding that the outcome of measuring the same observable twice in a row on the same state is getting the square of the eigenvalue if and only if the state is an eigenstate of the ...
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460 views

The location of an object is gauge dependent. Therefore, it's not measurable?

The location of an object $x$ depends on how we choose our coordinate system. If we move the zero point, $x$ also changes. However, since we have translational invariance, we can always do such shifts ...
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Is there a quantum analogue of Mean Value Theorem theorem?

Background I was thinking of Mean Value Theorem in the context of classical mechanics I have $2$ points $A$ and $B$ and my particle goes from $A$ to $B$ then I know the velocity of the particle at a ...
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Significance of eigenvalues of an observable Of a wavefunction [closed]

What really is meant by eigenvalue of an observable? Does it mean that everytime we measure a value of an observable the result obtained is equal to the eigenvalue of the observable?
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What is a quantum number in a quantum field theory?

In non-relativistic quantum mechanics, quantum numbers are associated with eigenvalues of an operator. For example, $\ell$ is a quantum number associated with the eigenvalue $\ell(\ell+1)\hbar^2$ ...
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Under what circumstances are general relativistic coordinate transformations physically meaningful?

Although the field equations of GR are covariant under arbitrary coordinate transformations, such as the transformation given by Dirac (in Princeton Landmarks pp 34) that eliminate the singularities ...
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1answer
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Relationship between the Galilei Group and the Phase Space

This question is kind of a follow up question to my last question on the need for canonical commutation relations and conjugate observables. A comment from Valter Moretti suggested that, given a ...
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2answers
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I have a question about momentum and energy of the infinite square well in quantum mechanics

In Griffiths quantum mechanics, There is a problem that "Find the momentum-space wave function $\varphi(p,t)$ for the $n$th stationary state of the infinite square well." The $n$th stationary ...
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Observer's effect and the Heisenberg choice

Quantum Mechanics postulates that the act of observation affects the behavior of the observed object.The most common example of this feature is the fact the unobserved object(e.g. a photon) behave ...
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Average value of non-projective observables

I am quite confused about how to measure observables (like Pauli spins). For example, in the exercise 2.66 of Nielsen and Chuang's textbook: Show that the average value of the observable $X_1Z_2$ ...
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Confusion about why deducing pointer observable from the structure of the Hamiltonians is not practical

I am trying to learn Zurek's theory of decoherence. Right now I am reading Decoherence, einselection and the existential interpretation (the rough guide) which seems like an easier read than his big ...
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7answers
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What do positions in Schrodinger Equation mean (Remember: the particle never has definite position)?

In position or configuration representation, the Hamiltonian operator, and thus the Schrodinger Equation, is expressed in terms of positions. But the particle never has definite position, what do ...
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Is there a way to measure this observable in QM?

Let a quantum system be described by Hilbert space $\mathscr{H}$ and let $|\psi\rangle$ be an arbitrary state. Define the operator $$P=|\psi\rangle\langle \psi|$$ This is hermitian. It has two ...
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1answer
182 views

What is the physical meaning of expectation value of the Hamiltonian operator?

I've been studying David Griffiths' Introduction to Quantum Mechanics and int that, it was explained that the expectation value of position $x$ is the average of the positions of $N$ identically ...
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A moment of cohomology$.$

As is well-known (cf. Ref.1), the momentum operator is defined up to a time-independent closed form. More precisely, the physically inequivalent momentum operators are classified by the de Rham ...
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189 views

No sense in the expression $\hat{x}| 1\rangle=\sqrt{\frac{2}{a}}\int_{-\frac{a}{2}}^{\frac{a}{2}}x\cos\left(\frac{\pi}{a}x\right)dx=0$

I am considering a particle of mass m in a symmetric infinite square well of width a in the fundamental state. $$V(x)= \begin{cases} 0 & \mbox{$|x|<\frac{a}{2}$} \\ \infty & \mbox{...
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1answer
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Why do we say spin/angular momentum is observable even though its components can't be determined simultaneously?

Why do we say spin or angular momentum of a particle is observable even though all of its components can't be determined simultaneously? For example, we can measure the $\hat{L_x}$ of a particle's ...
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Quantum Observation

Bear with me if I present a lack of knowledge - QM is not my field. There's a common notion in QM that until a particle is observed (measured), its properties are not definite, but rather are spread ...
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Identify a $|Ψ(0)⟩$ with $A|Ψ(0)⟩≠a|Ψ(0)⟩$ $\forall$ $A$ & $|Ψ(0)⟩=\sum a_j\lvert\chi_j\rangle$ for some $A$ and its eigenstates$\lvert\chi_j\rangle$

Is it possible to put a quantum system in a state at time $t=0$, which is not the eigenstate of any observable, but at the same time can be linearly expanded using the eigenstates of some observable? ...
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Doubt about fifth postulate of QM degenerate case

I think I didn't not really understand a comment found on "Quantum Mechanics" by Claude Cohen-Tannoudji. Talking about the fifth postulate of quantum mechanics in the case in which $a_n$ is a ...
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Generalisation of the measurement postulate in quantum mechanics

Given an observable that has a partially discrete and partially continuous spectrum of eigenvalues associated to it with the order of the spectrum's degeneracy being greater than 1, how would you ...
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2answers
114 views

Are total cross-sections useful (experimentally verifiable) observables?

I understand that differential cross-sections such as $$\frac{\partial \sigma}{\partial \Omega}\left(\theta,\,\phi\right)$$ are useful observables. But if we only know $\sigma_{\text{total}}$, the ...
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Definition of physical quantities

Physical quantities are often defined in textbooks as measurable quantities. I find this definition confusing. For example, if you think about it, the number of clothes in a cupboard is also a ...
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1answer
94 views

Measurement of position in quantum mechanics

I know that when you perform a measurement of position in quantum mechanics, the wave function collapses to something proportional to it, but in a small range of values of positions, depending on the ...
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1answer
137 views

What is the relation between a measurement and an observable?

Observables are represented by Hermitian operators. First of all, it's a little strange (to me) that some measurable physical quantity is represented by a transformation (or linear map), given that I ...
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1answer
50 views

What experiments can measure the eigenvalues of the particle exchange operator

In a system with two indistinguishable particles, the eigenvalue to the particle exchange operator $\hat{P_{ij}}$ is $+1$ if the two particles are exchange symmetric, ie. bosons, and $-1$ if they are ...
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Physical quantity related to the parity operator

There is a statement in quantum mechanics that for every physical quantity, there exists a Hermitian operator. The converse is also true. So the question is, what physical quantity is related to the ...
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1answer
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How to show that $\int\nabla^2\psi_n (x)\overline{\psi_m (x)}dx=0$ [closed]

Let us consider the three-dimensional time-dependent Schrödinger equation that has the general solution $\psi(x,t)=\sum_n c_n\psi_n(x)e^{-iE_nt/\hbar},$ where the functions $\psi_n$ are orthogonal. ...
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Simultaneous measurement of two observables

In quantum physics the configuration of a particle is fully defined by it's wave function. When a measurement of a particular observable ( eg. position, angular momentum etc.) is made on the particle ,...
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Eigenfunctions of observables

Are eigenfunctions of observables solutions to the time-dependent Schrödinger equation? Or is this not necessarily the case? From what I had been reading they are not necessarily solutions to ...
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257 views

Question about Charge and Gauge Transformation

Does gauge invariance imply charge neutrality? I understand that all physical observables must be gauge invariant. Does this mean that physical observables must be neutral? If a quark is in red, a ...
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1answer
70 views

Observer independent quantities in special relativity

I have been thinking about what things about a point particle do all observers agree about? And I thought trajectories of particles must be the same for all observers, right? But, clearly it is not. ...
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1answer
173 views

Time ordered product of bilinear functions for Dirac-field

If we have two Observables (bilinears of Diracfield $\psi(x)$) $O_1(x)=\bar{\psi}(x)\Gamma_1\psi(x)$ and $O_2(y)=\bar{\psi}(y)\Gamma_2\psi(y)$ and if we calculate their time ordered product $T(O_1(x) ...
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$C^*$ algebra of observables for a particle in a ring

It is known that for a free particle in $\mathbb{R}$, the $C^*$ algebra of the observables is given by the Heisenberg algebra i.e. generated by $p,q$ such that $[q,p]= i$ ($h=1$). For technical ...
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How do expected values of observables depend on the current state?

I'm currently looking into quantum computing following the book The Nature of Computation. On pages 835/836 they define observables and the expected value of an observable corresponding to a hermitian ...
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2answers
272 views

Basis of eigenvectors common to H and B

Considering a three-dimensional state space spanned by the orthonormal basis formed by the three kets $|u_1\rangle,|u_2\rangle,|u_3\rangle $. In the basis of these three vectors, taken in order, are ...