2
votes
1answer
76 views

Normalization of a wavefunction that's superposition of two unknown energy eigenfunctions

Question:$$\psi(x)=A(3u_1(x)+4u_2(x))$$where $u_1(x)$ and $u_2(x)$ are energy eigenfunctions. How to normalize function $\psi(x)$? My intuitive solution: I got ...
4
votes
2answers
68 views

Should the eigenkets be weighted in $|P\rangle = \sum\limits_{r}|\xi^r\rangle$?

Page 37 of Dirac's book The Principles of Quantum Mechanics, states The condition for the eigenstates of $\xi$ to form a complete set must thus be formulated, that any ket $|P\rangle$ can be ...
2
votes
2answers
68 views

Is it possible that we have a physical state which is a mixture of discrete eigenstates and continuous ones?

For a system has both continuous and discrete spectrum, is it possible that a physical states is something like: ...
15
votes
4answers
649 views

Why do electrons in an atom occupy only the stationary states?

When we talk about the elementary problems in quantum mechanics like particle in a box, we first calculate the energy eigen-function. Then we say that the most general state is the linear combination ...
4
votes
3answers
268 views

How is a bound state defined in quantum mechanics?

How is a bound state defined in quantum mechanics for states which are not eigenstates of the Hamiltonian i.e. which do not have definite energies? Can a superposition state like ...
2
votes
1answer
59 views

What is a virtual state?

In quantum mechanics / Raman spectroscopy, what is a virtual state? What is the difference between a virtual state and a superposition of states? Can you simply think of the virtual state as a ...
1
vote
2answers
59 views

Does the superposition principle affect the space of quantum states?

I am confused about the set of quantum states. I have seen it written that in classical physics, the set of all states is a simplex. (I think this refers to the probability simplex.) In quantum ...
4
votes
2answers
145 views

What is the physical reason behind linearity of Schrodinger's equation?

What is the physical reason for Schrodinger equation to be linear? Though in physics many interactions or dynamics are found non linear.
0
votes
2answers
74 views

Using bra-ket notation?

Am I using Bra-ket notation correctly? I want to define a superposition of the states, $|0\rangle$ and $|1\rangle$. Is it simply? $|0\rangle + |1\rangle$ I can't find any non-technical information ...
1
vote
2answers
69 views

Quantum Eraser thought experiment with light photons of distinct color

I tried to recreate the Quantum Eraser experiment into a thought experiment with a few changes. It left me a little perplexed as to what outcomes I should expect. Any help would be appreciated. Lets ...
0
votes
3answers
65 views

Can we apply Quantum Superposition

Erwin Schrödinger’s famous thought experiment's video presented by Perimeter Institute for Theoretical Physics. From this video can we conclude that , in a macroscopic label we can not have a ...
3
votes
3answers
244 views

Why are the energy eigenstates realized in atomic transitions?

I have a question like "Why is it often assumed that particles are found in energy eigenstates?", it is a little different, though. When one solves the hydrogen atom, one can use a polynomial Ansatz ...
0
votes
2answers
43 views

Superpositions and expectation values in quantum mechanics

When the wavefunction of a particle is not an eigenfunction of an operator, the property to which the operator corresponds does not have a definite value, Why? Also consider a linear combination of ...
2
votes
2answers
52 views

Could there be a correlation between the earth's magnetic field and quantum superposition

I do apologise in advance for what might seem like a stupid question coming from a non-physicist. But I was wondering if the earth’s magnetic field could influence the wave pattern that one observes ...
1
vote
3answers
63 views

Superposition principle

If $S=(v_{1},v_{2}......v_{n})$ is a basis for vector Space V, then every vector v in V can be expressed in the form of $v=c_{1}v_{1}+.......c_{n}v_{n}$ in an unique way. Explain the significance of ...
1
vote
2answers
87 views

What is the cut-off for quantum superposition?

Is there an explanation as to how macro objects aren't in superposition? At what size do objects stop being in a state of superposition?
1
vote
2answers
119 views

Has a photon or electron ever been observed in a state of superposition?

Has subatomic particles ever been seen in a state of superposition or do we just detect information like qubits about the state of the particle? So is actual matter in superposition or is it just ...
0
votes
0answers
32 views

Experimental proof of the principle of superposition in QM [duplicate]

I have read that we need all operators in QM to be linear to confirm the principle of superposition which is experimentally well proven. I wonder how such an experiment could be made?
1
vote
0answers
107 views

Beginner Quantum Mechanics Questions and Theories [closed]

So, I recently read the following article: http://www.preposterousuniverse.com/eternitytohere/quantum/ and I have some questions on some of the things it discussed, as well as some theories of my ...
0
votes
1answer
37 views

Probablilites for wave function collapse

From what I understand, superposition is when two states exist in all of their possible forms simultaneously until the moment of wave function collapse, when they essentially reduce into a single ...
1
vote
2answers
80 views

Under what circumstances is observing a superposition possible?

According to Ian Stewart's 2013 Symmetry: A Very Short Introduction (pp. 119-120), Experiment and theory suggest that superposed states should not be observable as such; only individual ...
0
votes
1answer
60 views
4
votes
1answer
363 views

What exactly does Aaron D. O'Connell's experiment show?

I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :- ...
1
vote
1answer
150 views

Are we so sure about superposition?

Apparently particles can be anywhere when not observed. How strong is this theory really? Okay the wave-function can be collapsed through observation but how are we so sure that when an object is not ...
1
vote
1answer
117 views

When do we see particles to be in a superposition of energy states?

I have two doubts: Exactly when does this happen? and If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3? ...
3
votes
1answer
144 views

Schrödinger's cat and the difficulty of macroscopic superposition state

The Schrödinger's cat was regarded as peculiar since we seldom encounter a superposition state in macroscopic scale: $$ | \mathrm{dead \,\,cat} \rangle + | \mathrm{alive \,\, cat}\rangle $$ We more ...
0
votes
1answer
87 views

Can a particle in superposition act as x*(energy?)

I can't find an answer anywhere - I even asked my physics teacher, he hasn't a clue. Is superposition an illusion, or can a particle literally act as [x] particles?
3
votes
1answer
232 views

Bra-ket notation, Bits, & Superposition

I am a quantum computing enthusiast, and recently I stumbled upon this the following two propositions: $$ \alpha|1\rangle + \beta|0\rangle$$ What does this mean? My understanding of this is that: ...
11
votes
4answers
1k views

Schrödinger's cat; why was it necessary?

Could someone please explain to me the idea that Schrödinger was trying to illustrate by the cat in his box? I understand that he was trying to introduce the notion of the cat being both alive and ...
0
votes
0answers
114 views

Superposition and density matrix. What are these states?

I just wanted to understand the following. Let's stay with the harmonic oscillator in QM, just to have an example at hand. First, there are all the different states for $n=1,2,...$. (Let's call them ...
1
vote
1answer
100 views

Linear Operators and their representations

I am currently learning Quantum mechanics on a slightly advanced level. I am curious in knowing if there are Linear Operators (Linear Maps) in the Hilbert Space (finite dimensional ones) that don't ...
0
votes
1answer
67 views

Quantum likelihood ratios?

Sorry if this is a dumb question, but I'm only starting to get to grips with this quantum malarkey. Anyway... Suppose I have two friends, Alice and Bob, both of whom have a random number generator. ...
0
votes
2answers
220 views

What's an atomic superstate/superposition, and how is it possible?

What's an atomic superstate/superposition, and how is it possible? I understand the basics - being something can be moving and staying still at the same time; the observer changes the behaviour - but ...
0
votes
0answers
67 views

Quantum eraser double slit experiment

In the quantum eraser double slit experiment, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?
0
votes
2answers
107 views

Basic Quantum Superposition

I'm looking to improve my understanding of quantum superposition. Consider the two-slit setup, where $|A\rangle$ is the state of the electron at the source, $|z\rangle$ is the state at some point on ...
1
vote
1answer
59 views

Spin half for the value of $|1 0\rangle$?

Spin-1/2 The eigenspinor , $X=aX_++bX_-$ $$X_+=\left( \begin{array}{cc} 1\\ 0\end{array} \right) $$$$X_-=\left( \begin{array}{cc} 0\\ 1\end{array} \right)$$ They are define like this because they ...
6
votes
6answers
2k views

How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
3
votes
1answer
131 views

Superpositions with two observers

This is a bit of an odd question. I'm not a physicist, so bear with me if I say something wrong. Lets say you have some sort of quantum event where matter is in a superposition. Standing next to you ...
0
votes
1answer
648 views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
3
votes
2answers
343 views

Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
4
votes
1answer
2k views

Differences between pure/mixed/entangled/separable/superposed states

I am currently trying to establish a clear picture of pure/mixed/entangled/separable/superposed states. In the following I will always assume a basis of $|1\rangle$ and $|0\rangle$ for my quantum ...
-3
votes
1answer
106 views

Superposition and the Winning Jackpot Numbers

Let's say I buy myself a lottery ticket (Mega-Millions). I have $\frac{1}{175,711,536}$ chance of winning. Before I tune on the tv/radio and listen to the winning numbers (i.e. make an observation), ...
2
votes
1answer
519 views

How do we know superposition exists?

How do we know superposition exists? Has it been observed, or has it been deduced, and how certain are we? The Copenhagen Interpretation seems to imply that superposition collapses into one state ...
1
vote
1answer
305 views

Can we use intensities in the superposition principle?

In using the superposition principle to calculate intensities in interference patterns, can we add the intensities of the waves instead of their amplitudes? I think that amplitude account for the ...
3
votes
4answers
330 views

Is this statement about quantum mechanics valid?

In Philosophy of Language by William G. Lycan, there are the lines: Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
2
votes
2answers
210 views

What does the Copenhagen interpretation say about the position of a particle before measurement?

Suppose there is a particle in space. When we measure the position of that particle, we get a particular value with a probability that can be calculated from the wave function. But, according to the ...
0
votes
2answers
229 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
1
vote
1answer
2k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k} $$ What i dont ...
2
votes
2answers
968 views

Is Schrödinger’s cat misleading? And what would happen if Planck constant is bigger?

Schrödinger’s cat, the thought experiment, makes it seem like as if measurement can cause a system to stop being in a superposition of states and become either one of the states (collapsed). So does ...
1
vote
4answers
658 views

Do multiple electrons exist during superposition?

Wikipedia says: Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically ...