# Tagged Questions

A linear operator (including a matrix) acting on a non-zero *eigenvector* preserves its direction but, in general, scales its magnitude by a scalar quantity *λ* called the *eigenvalue* or characteristic value associated with that eigenvector. Even though it is normally used for linear operators, ...

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### Determine the number of bound states admitted in Schrodinger system

Is there a general method for determining the number of bound states admitted by a potential in the Schrodinger equation? Certainly the number of dimensions must factor in somehow: the delta ...
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### Physical meaning of eigenvectors of mass matrix

What is the physical meaning of the eigenvectors of the mass matrix? If I consider a 2-dof system with one mass linked to two orthogonal springs and I write the equations in any orthogonal system of ...
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### Decompose a Hermitian Operator into Eigenvalues and Projectors

Quantum Computing - A Gentle Introduction by Eleanor Rieffell and Wolfgang Polak states on p57 : Any Hermitian operator $O$ with eigenvalues $\lambda_j$ can be written as $O = \sum_j \lambda_j P_j$...
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### Difference between operators used to represent quantum gates vs that to represent physical observables?

I have learnt that informations about a physical observable property is buried in the state vector of a quantum system. To get the possible value of a property all we need to do is multiply the state ...
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### Intuitive way to think about discrete energy levels

I'm currently taking an introductory quantum mechanics course and we just finished learning about the infinite square square well scenario. I understand all the maths used for calculating the ...
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### Eigenvector of spin half particle in applied magnetic field at angle

I am very new to this field of physics so sorry if this is basic. I was recently trying understand how you go about calculating energy splits of electrons in applied fields. I understand that given a ...
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### Non-scalar-valued eigenvalues

In quantum mechanics, an operator $\hat{O}$ is related to its eigenkets $|o_i\rangle$ via the relation $$\hat{O}|o_i\rangle = o_i |o_i\rangle$$ The eigenvalues $o_i$ gives the result of measuring the ...