Yarden Sheffer
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Commutator and Taylor series in quantum mechanics
10 votes

This is simply an identity of Taylor expansion and has nothing to do with the fact that you have operators around, if $$f(x)=\sum_n \frac{f^{(n)}(0)}{n!}x^n$$ then $$\frac{df}{dx} = \sum_n \frac{f^{(n+...

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Are self-consistency arguments logical/rigorous? An example with Pauli paramagnetism
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3 votes

The gist of such self-consistent is the (implied) assumption of a unique solution. If we indeed have a unique solution then the self-consistent solution we find under certain assumptions is indeed the ...

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Energy Mean Value of Quantum Gas
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3 votes

At low temperatures ($\beta\to\infty$) the partition function is dominated by the ground state and the average energy should be the ground state energy. This should be correct when taking the limit on ...

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How can we be sure, that the dot-product of the four-vectors $U$ and $A$ in special relativity is zero?
3 votes

Dot product of $u$ with itself is constant: $$u\cdot u=-c^2$$ Taking derivative with respect to proper time on both sides gives $$u\cdot \frac{du}{d\tau}=u \cdot a=0$$

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How can I use the Navier-Stokes equation to model the diffusion of a gas with the data I gathered?
2 votes

The short answer for 1: you can't. Long answer: While the NS are exact equations, getting useful information about transport in air strictly from the equations is unfeasible. The reason is that the NS ...

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How far does the Pauli Exclusion Principle go?
1 votes

The PEP is a direct result of the fermionic statistics of the neutrons. The fact that they are fermions mean that if we write a multiparticle wave function it must satisfy $$\psi(x_1,...,x_i,...,x_j,.....

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How should I solve the Schrödinger equation by diagonalization in QFT?
1 votes

Assuming that I understand the question correctly, the answer is not specifically about the AIM, but in general about second-quantized operators. The crucial thing to understand is that the ladder ...

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Does the first-order energy correction in the degenerate case equals to the eigenvalues of the perturbation matrix?
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1 votes

The relevant matrix that you need to diagonalize is not $\delta H$ itself, but its projection onto each one of the degenerate subspaces of $H_0$. Since the $E=1$ subspace is generated by $v_1=(1,0,0,0)...

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Examples of the physical significance and importance of matrix diagonalization and eigenvalues for first year undergraduates?
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0 votes

This is not a physics application per se, but I remember that as a first year undergrad I was convinced in the usefulness of matrix diagonalization by the application to obtain a closed expression for ...

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Using Schwarz's Inequality to show an expectation value relationship of a particle
0 votes

For the Cauchy-Schwartz inequality you need to have some inner product that you can use. The inner product you used $$\left\langle f,g\right\rangle=\int f(x)g(x)dx$$ is valid, but the definition $$\...

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Particle in ring zero energy?
0 votes

My guess is that by "violation of HUP" you mean that $$\left\langle \theta^2\right\rangle\left\langle L_z^2\right\rangle=0$$ The reason for that is that while we can define the operator $L_z=...

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