Questions tagged [wavefunction]
A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state. DO NOT USE THIS TAG for classical waves.
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About the complex nature of the wave function?
1.
Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
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Why is it impossible to measure position and momentum at the same time with arbitrary precision?
I'm aware of the uncertainty principle that doesn't allow $\Delta x$ and $\Delta p$ to be both arbitrarily close to zero. I understand this by looking at the wave function and seeing that if one is ...
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Does Heisenberg's uncertainty under time evolution always grow?
Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
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Why isn't the universe full of electrons?
The probability of an electron found outside the atom is never zero. Consider building an electron detector, it must receive permanent signals from all electrons in the universe, as they can exist ...
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Hilbert space vs. Projective Hilbert space
Hilbert space and rays:
In a very general sense, we say that quantum states of a quantum mechanical system correspond to rays in the Hilbert space $\mathcal{H}$, such that for any $c∈ℂ$ the state $\...
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Normalizable wavefunction that does not vanish at infinity
I was recently reading Griffiths' Introduction to Quantum Mechanics, and I stuck upon a following sentence:
but $\Psi$ must go to zero as $x$ goes to $\pm\infty$ - otherwise the wave function would ...
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What exactly is a bound state and why does it have negative energy?
Could you give me an idea of what bound states mean and what is their importance in quantum-mechanics problems with a potential (e.g. a potential described by a delta function)?
Why, when a stable ...
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What's the point of Pauli's Exclusion Principle if time and space are continuous?
What does the Pauli Exclusion Principle mean if time and space are continuous?
Assuming time and space are continuous, identical quantum states seem impossible even without the principle. I guess ...
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The formal solution of the time-dependent Schrödinger equation
Consider the time-dependent Schrödinger equation (or some equation in Schrödinger form) written down as
$$
\tag 1 i\hbar \partial_{t} \Psi ~=~ \hat{H} \Psi .
$$
Usually, one likes to write that it has ...
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What is the probability for an electron of an atom on Earth to lie outside the galaxy?
In this youtube video it is claimed that electrons orbit their atom's nucleus not in well-known fixed orbits, but within "clouds of probability", i.e., spaces around the nucleus where they can lie ...
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Why doesn't the nucleus have "nucleus-probability cloud"?
While deriving the wave function why don't we take into the account of the probability density of the nucleus? My intuition says that the nucleus is also composed of subatomic particles so it will ...
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Half-integer eigenvalues of orbital angular momentum
Why do we exclude half-integer values of the orbital angular momentum?
It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
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Can someone provide a physical -- not mathematical -- intuition for the phase in a quantum wavefunction?
I've read every thread on StackExchange (and Quora and reddit...) that I can find about a physical intuition for the phase in the quantum wave function, and I still Just. Don't. Get. It. (Yes, I've ...
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The meaning of the phase in the wave function
I have just started studying QM and I got into some trouble understanding something:
Let's say there is a wave function of a particle in a 1D box ($0\leq x\leq a$):
$$\psi(x,t=0) = \frac{i}{\sqrt{5}}...
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What is a wave function in simple language?
In my textbook it is given that
'The wave function describes the position and state of the electron and its square gives the probability density of electrons.'
Can someone give me a very simple ...
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