All Questions
Tagged with wavefunction probability
328
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Quantum Mechanical Current Normalisation
Consider an electron leaving a metal. The quantum-mechanical current operator, is given (Landau and Lifshitz, 1974) by
$$
j_x\left[\psi_{\mathrm{f}}\right]=\frac{\hbar i}{2 m}\left(\psi_{\mathrm{f}} \...
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What Does Feynman Mean When He Says Amplitude and Probabilities?
In Feynman lectures on gravitation section 1.4, he tries to debate over whether one should quantize the gravitation or not.
He provides a two-slit diffraction experiment with a gravity detector, which ...
- 529
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3
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Is the zero vector necessary to do quantum mechanics?
Textbook quantum mechanics describes systems as Hilbert spaces $\mathcal{H}$, states as unit vectors $\psi \in \mathcal{H}$, and observables as operators $O: \mathcal{H} \to \mathcal{H}$. Ultimately, ...
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Physical meaning of each term of the square modulus of a wave function
The expression below is the square modulus of the wave function of a harmonic potential ($V=\frac{1}{2}m\omega^2 x^2$) in which it's stated that the probability of finding the particle in the $\psi_0$ ...
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Infinite potential well suddenly expanding
Problem statement: an electron is in its fundamental state in an infinite (1-dimensional) potential well, its walls being located at $x=0$ and $x=a$. Suddenly, the right wall moves from $x=a$ to $x=2a$...
- 1,616
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Momentum probability density and its normalization
Let the (normalized) wave function $\Psi(x,y)$ represent a free particle in the XY plane. I know $|\Psi|^2$ gives me the probability density function of the particle's position, which I can then ...
- 1,616
-3
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Does the inner product of wavefunctions really have units? [closed]
Let $\psi(x)$ and $\phi(x)$ be wavefunctions. I usually see the inner product defined as
$$\int dx\, \overline{\psi(x)} \, \phi(x)$$
and interpreted, I think, as "the amplitude that state $\phi$ ...
- 120
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93
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What is the relationship between an electron's wave-like and particle-like qualities? Is "Electrons are waves and particles" the whole truth? [duplicate]
Upon researching the double-slit experiment, it seems to me that electrons are somehow cloaked in wavelike behavior (not at all like my previous idea that electrons were waves and somehow were also ...
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73
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Why is psi square a possibility? [duplicate]
Is psi square just an assumption? Or there is a physical reason why they defined like that? My procedure is:
It is intuitive for me to think possibility is proportional to energy distribution. ...
김건형
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Can the probability of finding a particle in a certain finite region be zero?
Don't worry this time isn't about doubleslit but I'll still use it for my question.
Imagine an electron is emitted from the source and I shall allow a certain amount of time to lapsed so as to provide ...
- 13k
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Probability current density of gaussian wavepacket
This was the question that was asked in an exam.
For a gaussian wavepacket $$ \psi(x,t) = Ae^{\frac{x^2}{4a^2}}e^{i(k_0x-\omega_0t)} $$ corresponding to a free particle, (i) Find the probaibility ...
- 353
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78
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Why classical probability is insufficient for quantum mechanics
I've started reading Brian Hall's Quantum Mechanics for Mathematicians. He gives a motivation for the operator formalism for quantum mechanics. If you think of position of a particle as a random ...
- 141
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178
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Most probable position of finding an electron represented in cartesian and spherical coordinates
Consider the probability of finding an electron within a region:
$$P= \iiint |\psi(x,y,z)|^2 dxdydz$$
I would think that The probability of finding an electron at a single point in space would be ...
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What if probability current is independent of position and time? [closed]
I worked an example in Griffiths to find probability current and then determine the direction of the flow of probability. As you can see the $J$ is constant value and independent of time and position $...
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What is the interpretation of these hydrogen probability density diagrams?
In the diagram above, what is the interpretation of all of the individual renders? Does the hydrogen atom continuously change between these states? For example, will $(n, l, m_l)$ become $(2, 0, 0)$ ...
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