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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Uncertainity in position in 1D potential box
In a question of a usual 1D box for a particle between $-L/2$ to $L/2$ i had to compute $\Delta x$ and $\Delta p$ for the particle. The solution used the formulas-
$$\Delta x = \sqrt{\langle x^2 \...
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How do you apply a transformation, or a superposition in David Hetens' geometric formulation of the wavefunction?
In David Hestenes' formulation of the wavefunction in geometric algebra, we have:
$$
\psi(x) = \sqrt{\rho(x)} R(x) e^{-ib(x)/2}
$$
where R(x) is a rotor.
For simplicity, let us now consider a two-...
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How to Perform Fourier Transform on a Quantum State of Spin-1/2 Particle?
I am currently studying quantum mechanics and need help understanding how to perform the Fourier transform of a particular state. I have a spin-1/2 particle whose momentum and spin state at time $t=0$ ...
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Incorrect factor in radial wavefunction $R_{2,1}$ of hydrogen atom
First of all, let me state that this isn’t a homework question but rather my personal annoyance. I can provide a proof in the comments if you think otherwise. The general equation for radial wave ...
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Density Matrix vs Wavefunction Formalism
What is the main motivation and advantages of the density matrix formalism compared to the wavefunction formalism? From what I understand, the density matrix is more commonly used when you want to ...
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A missing link in the logical chain about the Aharonov-Bohm effect
The usual treatment of the Aharonov-Bohm effect (which appeared already in Aharonov and Bohm's original paper) takes two particular local solutions of the Schrödinger equation, $\psi_1$ and $\psi_2$. ...
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Reflection of quantum particle colliding with a potential barrier
Let a quantum particle be subject to a one dimensional step potential barrier $V$ such that:
$$V(x)=\begin{cases}0, \ x<0 \\ V_0, \ x>0\end{cases}$$
where the particle's energy is $E>V_0>0$...
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Amplitude superposition for different kinds of particles
We have seen that the probability of finding a particle at a particular point is the square of its wave function. In the double slit experiment, we notice that wave functions add up and the resultant ...
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How to decide for correct value of phase difference?
A sinusoidal wave is propagating along a stretched string that lies along x-axis. The wave is moving in +x-direction. Figure shows the graph of transverse displacement of particles of the string at x =...
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Are reflection and transmission coefficients in 1D problem are independent of the direction in which we choose as incident?
I was watching a lecture series of Quantum mechanics of Professor V. Balakrishnan,
There was a problem session,
“For an arbitrary potential barrier (any potential function of position and it need not ...
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Why do delta wells and delta barriers behave equivalently, but normal wells and normal barriers don't?
In Griffith's Intro to QM, it is shown that for $V(x)=-\alpha \delta(x)$ regardless of whether $\alpha$ is positive (a "delta well") or negative (a "delta barrier"), the ...
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Operators algebra for quantum mechanics [closed]
I am taking my first quantum mechanics course and I am a bit lost in operators algebra. These are the main questions I have:
Why can we write this kind of equations? $$ Ô \psi = o\psi $$
What I mean ...
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Confusion in de Broglie wave and wave function
Recently I saw some questions related to the same topic and got to know that matter-wave functions(Ψ) are superpositions of multiple de Broglie waves corresponding to multiple momenta, which is ...
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Difference between the expectation value of an operator and operator applied to wave function?
Expectation value of any operator $\hat{Q}$ is defined as,
$$
\left\langle\psi_n\mid\hat{Q}\mid \psi_n\right\rangle
$$
and action of the operator $\hat{Q}$ on wavefunction is defined as
$$
\hat{Q} \...
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Schroedinger equation with value of wave function in polar coordinates?
I'm trying to get a better sense of what causes an increase in the magnitude and phase of the wave function at a given point. Is there a way to rewrite the schroedinger equation such that it ...
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