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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Continuity & smoothness of wave function
Is there anything physical that enforces the wave function to be $C^2$? Are weak solutions to the Schrödinger equation physical? I am reading the beginning chapters of Griffiths and he doesn't mention ...
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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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How does the momentum operator act on state kets?
I have been going through some problems in Sakurai's Modern QM and at one point have to calculate $\langle \alpha|\hat{p}|\alpha\rangle$ where all we know about the state $|\alpha\rangle$ is that $$\...
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The formal solution of the time-dependent Schrödinger equation
Consider the time-dependent Schrödinger equation (or some equation in Schrödinger form) written down as
$$
\tag 1 i\hbar \partial_{t} \Psi ~=~ \hat{H} \Psi .
$$
Usually, one likes to write that it has ...
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How can I solve this quantum mechanical "paradox"?
Let a (free) particle move in $[0,a]$ with cyclic boundary condition $\psi(0)=\psi(a)$.
The solution of the Schrödinger-equation can be put in the form of a plane wave. In this state the standard ...
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Time-independent Schrödinger function: If the potential $V$ is even, then the wave function $\psi$ can always be taken to be either even or odd
I have done the Problem 2.1 in Griffiths' quantum mechanics,
and it seems not making sense to me.
What if the wave function isn't symmetric at all?
Then obviously the proof doesn't work. The ...
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Galilean covariance of the Schrodinger equation
Is the Schrodinger equation covariant under Galilean transformations?
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:...
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Relation between Wave equation of light and photon wave function?
Suppose in our double slit experimental setup with the usual notations $d,D$, we have a beam of light of known frequency $(\nu)$ and wavelength $(\lambda)$ - so we can describe it as $$ξ_0 = A\sin(kx-\...
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When Eigenfunctions/Wavefunctions are real?
When the Hamiltonian is Hermitian(i,e. beyond the effective mass approximation), generally under which conditions the eigenfunctions/wavefunctions are real?
What happens in 1D case like the finite ...
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Understanding Dirac's notation
Let's say I have eigenstates $|x\rangle$ associated with measurement of position. I know that the eigenstates corresponding to their respective eigenvalues form a basis, let's call it $A$. Now let's ...
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Normalizing the solution to free particle Schrödinger equation
I have the one dimensional free particle Schrödinger equation
$$i\hbar \frac{\partial}{\partial t} \Psi (x,t) = -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} \Psi (x,t), \tag{1}$$
with ...
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Bohr-Sommerfeld quantization condition from the WKB approximation
How can one prove the Bohr-Sommerfeld quantization condition
$$ \oint p~dq ~=~2\pi n \hbar $$
from the WKB ansatz solution $$\Psi(x)~=~e^{iS(x)/ \hbar}$$ for the Schroedinger equation?
With $S$ the ...
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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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Why the statement "there exist at least one bound state for negative/attractive potential" doesn't hold for 3D case?
Previously I thought this is a universal theorem, for one can prove it in the one dimensional case using variational principal.
However, today I'm doing a homework considering a potential like this:$...
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