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Results tagged with quantum-mechanics
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user 7924
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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Accepted
How do you assign an observable to spectral lines in Heisenberg's resolution of Rydberg-Ritz?
Spectral line frequencies are positive differences between eigenvalues of the hamiltonian. If the Hamiltonian is 4 by 4, there are 4 eigenvalues and therefore 6 positive differences (unless there are …
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2
votes
How can I prove this inequality?
The formula is positive homogeneous in the $\lambda_j~$. Thus it is enough to prove the result for $|\lambda_j|=1~$ for $j=1,2~$. For this case, the result follows from $|\lambda_1\phi_1-\lambda_2\phi …
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2
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Right topology for infinite dimensional "Hilbert" spaces with indefinite or semidefinite norm
The topology is imposed only on the physical Hilbert space, which has a positive definite metric.
If you need a topology outside, you are free to choose any that suits your purposes, but there is no …
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1
vote
Tensor product of Hilbert spaces and non-interacting particles
In classical mechanics, the phase space of a single particle consists of pairs $(q,p)$ of the position $q$ and momentum $p$ of the particle. In quantum mechanics, this is replaced by dropping either p …
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What is the spectrum of the Hamiltonian of the universe?
Assume that the universe is asymptotically flat and has finite total energy. (These appear to be the minimal assumptions under which talking about the Hamiltonian of the universe make sense.)
Then t …
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Accepted
What is the single particle Hilbert space?
The single-particle space depends on mass, spin, and other quantum numbers of the particle.
In general, a single-particle space is a positive energy irreducible unitary representation of the symmetr …
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2
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Expressing a unitary operator in terms of a Hermitian operator
As mentioned by dushya, Hermitian matrices are much easier to handle since they form a linear space. Unitary operators are far more difficult to construct (and to use outside of purely theoretical con …
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2
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Examples of discrete Hamiltonians?
There are different ways of getting discrete systems. Generally, there is a Hamiltonian that defines the unperturbed state of a system (e.g., an atom trap, or a quantum storage device). If the system …
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2
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Is there a quantum state for a large system
Quantum states of macroscopic systems are routinely considered in statistical mechanics. They used to derive both the thermodynamic properties of macroscopic materials and the way they deform and resp …
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2
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Which came first the decay or the emission?
Assuming ''a hydrogen atom in an infinite and otherwise empty universe'' makes your question meaningless. Your universe does not contain anything that could possibly induce the postulated perturbation …
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Measurement postulate on density matrix in a mixed state : is there a global transformation?
Note that the result must be independent of any decomposition of $\rho$ into a mixture of pure states since the latter is in principle unobservable.
The correct formula for the most general filtering …
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Really, what is the minimum number of postulates of quantum mechanics?
The point of a list is to give a simple memorizable starting point in terms of which one can organizing the innumerable additional details that come later.
Clearly, this can be done in different ways, …
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Why quantum states are classified using only conserved quantities?
It is not just a matter of symmetries, though the latter play an important role.
The rationale for the labeling is that one wants to have a simple basis for the Hilbet space of wavefunctions in which …
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Accepted
What determines which observables are QM?
Which superpositions are allowed or forbidden in principle is determined by so-called superselection sectors. http://en.wikipedia.org/wiki/Superselection
These are virtually absent from the standard t …
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3
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Is it possible to recover the old Bohr-Sommerfeld model from the QM description of the atom ...
Some version of Bohr-Sommerfeld quantization is exact for classically integrable systems (i.e., systems that have a fairly large symmetry group in a sense that can be made precise), and hence in parti …
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