Tagged Questions

The Born rule is a rule in Quantum Mechanics that states that the probability density $\rho$ is $|\psi|^2$ where $\psi$ is the probability amplitude.

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Question about interpreting probabilities in QM [duplicate]

For the example of an infinite square well, $\psi(x)=0$ for $x$ outside the well/interval, and we are to interpret this as the particle cannot be found outside the well because ...
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0answers
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Quantum decoherence and Schrodinger's equation

In non-relativistic quantum mechanics, the equation of evolution of the quantum state is given by Schrodinger's equation and measurement of a state of particle is itself a physical process. Thus, ...
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1answer
120 views

Was Max Born the first to notice a connection between quantum mechanics and randomness?

Max Born introduced the Born Rule in a paper from 1926. But was this really the first time that a connection between quantum mechanics and randomness was noticed? Today, quantum mechanics and ...
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2answers
78 views

Are there two aspects of Born's rule?

I am having some problem understanding Born's rule. I am getting a little bit confused. Here it goes; Let $f(x,t)$ be a solution of Schrodinger equation. Then Born's rule says that the square modulus ...
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1answer
68 views

Can you get Born probabilities that are irrational from an experiment?

Is it possible to design an experiment getting irrational number predictions (in practice, you can't actually measure infinite numbers of decimal points, obviously) for Born probabilities? If you ...
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1answer
105 views

Decoherence in Everett quantum mechanics

Take an initial state and its environment, $E$, as follows, $$ |\psi\rangle_i = |0\rangle |E\rangle + \sqrt{2}|1\rangle |E\rangle. $$ Suppose that I've written it already in the basis in which the ...
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5answers
660 views

Is there any operator behind probability, in quantum mechanics?

In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is ...
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3answers
265 views

Why is $|\Psi|^2$ the probability density?

I am starting with Quantum Mechanics, learning online. I can't seem to find the reason for $|\Psi|^2$ being the probability density of finding an electron. They've just taken it for granted ...
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2answers
111 views

Interpretation Klein-Gordon equation

What is the problem if we try to interpret KG equation as a single particle equation? Also I wish to know whether the born interpretation of wavefunction is applicable in relativistic quantum ...
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2answers
273 views

Interpretation: probability form probability amplitude (free particle)

If you compute the probability amplitude of a free 1D non-relativistic particle with mass $m$, located at position $x_0$ at time $t_0$, for beeing detected at some other point $x_N$ at time $t_N$ you ...
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1answer
242 views

Probability in Quantum Mechanics: General

How do I find the most probable value of position of a (non-Gaussian) wave function? Is it the same value as the expectation value of the position? And is it true that the most probable value of ...
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1answer
412 views

Why is classical physics not valid for a harmonic oscillator in its lowest energy state? [closed]

I am reading Born's interpretation of wave function in quantum physics by Eisberg & Resnick and I am not able to understand this description about comparison between the classical and quantum ...
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340 views

Real Part of the Wave Function

In Quantum Mechanics the square of the wave function is compared to a probability density. Is there no similar relation to waves in the sense that something meaningful can be ascribed to the real part ...
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2answers
223 views

How to understand wavefunction in quantum mechanics in math

I am reading some introduction on quantum mechanics. I don't understand all but I get the point that the wavefunction tells some probability aspects. In one book, they show one example of the ...
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3answers
708 views

Born's Rule, What is the Reason?

As far as I've read online, there isn't a good explanation for the Born Rule. Is this the case? Why does taking the square of the wave function give you the Probability? Naturally it removes negatives ...
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2answers
421 views

Born rule for photons: it works, but it shouldn't?

We can observe double-slit diffraction with photons, with light of such low intensity that only one photon is ever in flight at one time. On a sensitive CCD, each photon is observed at exactly one ...
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3answers
426 views

Could quantum mechanics work without the Born rule?

Slightly inspired by this question about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most ...
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2answers
247 views

Are probability-preserving variations of QT with respect to the Born rule mathematically possible?

Is it possible to create (m)any theoretically workable framework(s) - that do(es) produce probabilities - by taking QM and replacing the Born(-like) rule(s) with something that is not equivalent to it ...
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14answers
3k views

Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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5answers
610 views

Born rule and unitary evolution

Is the Born rule a fundamental postulate of quantum mechanics, or can it be inferred from unitary evolution?
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1answer
918 views

About Born's rule

I wanted to gain a better understanding of the Born rule to make my class on quantum mechanic feel less ad hoc. To do so I attempted to show that the version (1) given in my book is equivalent to the ...
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4answers
1k views

Why is Gleason's Theorem not enough to obtain Born Rule in Many Worlds Interpretation?

The Many Worlds interpretation suffer from at least 2 "wounds", the preferred basis issue and perhaps the most notorious probability issue. How do you make sense of probability in a model where ...
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3answers
745 views

Historical background of wave function collapse

I wonder what were the main experiments that led people to develop the concept of wave function collapse? (I think I am correct in including the Born Rule within the general umbrella of the collapse ...