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Results tagged with quantum-mechanics
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user 154632
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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Mathematical Representation of the Generator of Translation
Where does this expression come from? Why is the $N$ an exponent?
$J(\Delta x' \hat x) = lim_{N \to \infty} (1-\frac{ip_x\Delta x'}{N\hbar})^N $
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Expansion Coefficient - Why Does Sigma Disappear?
How is the second equation derived with the orthonormality property?
The orthonormality property is
< a"|a'> = kronecker delta_a",a'
I ask because I don't know why the summation in the first eq …
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Why is there a minus sign on the right hand side, when the ket flips?
How is the right hand side obtained from the left hand side in this equation?
$$ \int \mathrm{d}x' | x' + \Delta x' \rangle \langle x' | \alpha \rangle = \int \mathrm{d}x' | x' \rangle \langle x' - \ …
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Derivation of the Infinitesimal Translation Operator [duplicate]
$$J(d \vec x') = \left(1 - \frac{i \vec p \cdot d \vec x'}{\hbar}\right)$$
This is the infinitesimal translation operator, as defined on p. 46 of Modern Quantum Mechanics by Sakurai & Napolitano.
H …
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Expansion of an Eigenket
What is the purpose of multiplying only one base ket by $e^{i\theta}$, when expanding an eigenket as a linear combination of its base kets?
Example: $|S_x; +\rangle = \frac{1}{\sqrt2}(|+\rangle + |- …
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2
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Proving the orthogonaity property by using using the reality condition
I am reading Modern Quantum Mechanics by Sakuria and Napolitano.
Background Information from the Textbook
a' and a'' are eigenvalues of A.
A is a Hermitian operator.
The symbol, * , implies com …
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Proving the orthogonaity property by using using the reality condition
Now I realize: The reason why the reality condition is used to prove the orthogonality property is that one needs to consider the case for which the eigenvalues are the same before considering the cas …
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Dirac Notation: Why are these two expressions equal?
Consider
$$
\langle a''|(AB - BA)|a' \rangle = (a'' - a') \langle a''|B|a' \rangle
$$
where $a''$ and $a'$ are eigenvalues of observable, $A$, which is Hermitian (real eigenvalues). $A$ and $B$ are …
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Bra Ket Notation and Derivative [duplicate]
Let $$a$$ be the partial derivative symbol with respect to $x$. What is $$\langle x|a|x \rangle$$ equal to? I think it is 0 but not sure.
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Partial Derivative and Dirac Notation [duplicate]
Does the partial derivative of $\langle x'|\alpha\rangle$ with respect to $x'$ equal $|\alpha\rangle$? Why?
Note: $|\alpha\rangle$ is an arbitrary ket, $x'$ is an eigenvalue, and $\langle x'|$ is an …
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