# Tagged Questions

To be used for linear algebra, and closely related disciplines such as tensor algebras and maybe clifford algebras.

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### Please explain this project to me [closed]

I've been struggling with this project for a few months now and I frankly can't break out of my way of thinking. The questions I'm struggling with understanding are written down below. The questions ...
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### Relation between coherent states [closed]

Suppose $\left|\alpha\right\rangle$ and $\left|-\alpha\right\rangle$ be two coherent states. Is there any relation between them or are they completely different coherent states?
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### What is the difference between active and passive transformations in Quantum Mechanics?

I am trying to understand what each transformation means and what their differences are but many books that don't state which transformation they are referring to make it a bit confusing to understand ...
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### Basis/Projection Notation Question Quantum Mechanics

Lets say you have a inner product between two state vectors with an operator in between A|X|B. I can write this as a summation over I and j as A|i i|X|j j|B (sorry for notation). But I don't ...
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### Block Diagonal Matrix Shankar Quantum Page 45

On page 45 of Shankar's intro to qm (you can find a pdf of it online if you want) he says that a specific operator has a block diagonal form because when it operates on some element of an eigenspace ...
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### Commuting operators and Direct product spaces

Under what conditions is the common eigenspace of two commuting hermitian operators isomorphic to the direct product of their individual eigenspaces? When can an eigenket $|\lambda$1$\lambda$2$\rangle$...
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### Conservation of energy in the form of y=kx +b?

I am doing an experiment on method of mixtures and specific heat capacities. During my experiment I have to use the graph as a means of finding the SHC of the subject. So I did the experiment with ...
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### Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
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### Why do we use orthogonal axes?

I have been asked several times that “why do we use orthogonal axes in coordinate systems?” and I was always replying that “because of simplicity”. But, today morning, someone asked me that question ...
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### Resistance Distance in large electrical networks

I am not tremendously familiar with electrical circuits (I have some memories, but too long ago) and now I have come accross a problem where I need to compute the resistance distance in a graph. So, ...
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### What is the difference between a tensor, vector, and a matrix? [duplicate]

I'm currently going through notes on a physics course and I'm having trouble understanding the difference between a tensor, a vector, and a matrix. I know that a vector is a kind of tensor and that a ...
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### Signature of $f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \mathbb{R}$, $f(\omega, \omega') = \omega \wedge \omega'$ [closed]

Define$$f: \Lambda^2(\mathbb{R}^4) \times \Lambda^2(\mathbb{R}^4) \to \Lambda^4(\mathbb{R}^4) \cong \mathbb{R}, \quad f(\omega, \omega') = \omega \wedge \omega'.$$ What is the signature of $f$? ...
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### Diagonalisation: Schmidt vs eigenvalue - when to use which?

In physics we encounter diagonalisation of matrices or operators in a variety of areas. But there are different kinds, the main two being Schmidt decomposition and eigenvalue diagonalisation. The two ...
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### Negative powers of operators

This may sound like a strange question, but just to be sure: Suppose I have a general Hermitian operator in Hilbert space whose action on an eigenvector is given by $R|r\rangle = r|r\rangle$. Then, I ...