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The difference between statistical physics and quantum mechanics is that, in statistical physics, it is always reasonable to either measure a quantity, or demonstrate that the effect of that quantity can be bundled into an easy to work with random variable, often through the use of the Central Limit Theorem. In such situations, it can be shown that the ...


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Forget interpretations. The predictions of quantum mechanics - which agree with all interpretations (by definition of 'interpretation')- does not allow prediction of experimental/observational outcomes no matter how much information is gathered about initial conditions. (You can't even get the classical information needed in classical physics because of the ...


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Yes, the Probability current is defined as $$J(x,t)=\frac{i\hbar}{2m}\bigg(\Psi\frac{\partial \Psi^*}{\partial x}-\frac{\partial \Psi}{\partial x}\Psi^*\bigg)$$ If the scattering matrix is defined as $$ \begin{bmatrix} S_{11}&S_{12}\\ S_{21}&S_{22}\\ \end{bmatrix} $$ The transmission coefficient $T$ is given by $(S_{21})^2$, this is only true in ...


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This probably more a philosophical than a physical discussion. Let's take a simple everyday example: The air molecules in the room where you are sitting are fairly evenly distributed through the room. Because the molecules are subject to random motion, it's perfectly POSSIBLE to have all molecules bunch up in one half of the room and that there is a perfect ...


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I will address the title, ignoring the content of the question . If I repeated a quantum measurement, would it be the same? This is the method of gathering data in particle physics in order to check with as good an accuracy as possible the quantum mechanical predictions for the interactions. For example one sets up a beam of identical particles ...


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As you said, the result of the measurment depends on probability. Each eigenvalue (i.e. result of a measurment) has a certain probability of coming out when a some characteristic of the system is measured. Think of this in an easier example. Suppose that you have a pair of dice. Both are exactly the same, so, for both dice, the probability of each number to ...


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A "wave function" is a mathematical model (or representation) of a given wave. A "function" is represented by the symbol $f$. It can be a function of distance (x), time (t), space (r), etc. and is usually represented by an equation. If the equation represents a wave, then the function is a wave function. For example, a simple wave with constant amplitude ...


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Dice is a purely classical object, if one starts from a known boundary condition, the Newton's law differential equations should return you the same result every time. However, electrons are quantum object, in the sense that they are very fragile. Once you measure the position, i.e. shining light on the electrons, you impart momentum so that the result would ...


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Your question has no answer. There is no "why". It is a postulate of quantum mechanics that a pure state vector contains all information you can possibly know about a physical state. Note that this is not the same as saying it contains all information you can possibly imagine having about a physical state, particularly since your (and my) imagination is ...


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Technically one cannot say observables are probabilistic, since they are mathematically described by deterministic operators. Now when an observable has different eigenvalues, then the Born rule is used to predict which value the experiment will get, and this is where probabilities arise. The Born rule is a postulate of Quantum Mechanics, historically ...


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A very simple example of a wave function is y = sin x This might describe the momentary shape of a wave made by wiggling a rope. This shape would move along the x-axis with time, so y= Sin(x-t) would be a very simplified example of a moving sin wave I'm sure I will be dissed for answering your question literally. I do have 4 years of tertiary maths and 3 ...


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A wave function is a complex-valued function $f$ defined on ${\mathbb R}^1$ (if your electron is confined to a line) or on ${\mathbb R}^2$ (if your electron is confined to a plane) or ${\mathbb R}^3$ (if your electron ranges over three-space), and satisfying $$\int |f|^2=1$$ (where the integral is defined over the entire line or plane or 3-space). Every ...


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The wave function is the solution to the Shroedinger equation, given your experimental situation. With a classical system and Newton's equation, you would obtain a trajectory, showing the path something would follow: the equations of motion. For a quantum mechanical system you get a wave function, and the rules it obeys over time. With this you can determine ...


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You have confused counting worlds with computing probabilities. They are different things. If you measured $m$ systems identically prepared to give one of $n$ result $v_1,$ ...$v_n$ with respective frequencies $p_1,$ ... $p_n$, then there are $n^m$ aggregate outcomes. But the MWI doesn't predict different probabilities than any other interpretation. Both ...


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(I am not sure this is an answer but it is to long to be a comment) Let us create a simple example of a system of $3$ states, state $1$, state $2$ and state $3$. Let state $1$ and state $2$ both have an energy of $E$ and state $3$ have an energy of $E'\ne E$. Your first summation is summing over individual states. I.e. it is saying 'let us call the energy ...


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The absolute value of the $\Psi(x)$ describes the probability density. That means, you have to integrate it over the range you are interested in to get the total probability. If you are not familiar with these concepts, you should probably first understand them :) it is really more interesting to understand something deeply then just to talk about diffuse ...



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