Quantum Mechanics Quotes

“Take two systems. We’ll call them system described by the Hilbert space”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“3.5.3 Ehrenfest Theorem We can look at how the expectation value of some operator changes with time. We’ll assume that the operator itself has no time dependence”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“If we want to write down the analogous quantum Hamiltonian”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“We see that the Gaussian wavepacket is rather special: it saturates the bound from the Heisenberg uncertainty relation. The class of Gaussian wavefunctions”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“There is an algebraic way of formalising whether two observables can be simultaneously measured or whether”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“This means that if we have many systems”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“where is the exponential operator (3.105)”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“the Hamiltonian”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“A projection operator projects any state onto some subspace of . A projection operator is Hermitian”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“An eigenstate of a Hermitian operator obeys (3.66) where is the eigenvalue.”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“Not any old linear operator qualifies as a physical observable in quantum mechanics. We should restrict attention to those operators that are Hermitian.”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“Given an operator acting on some class of functions”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“In quantum mechanics”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“. However”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“​ Moreover”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“There are”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“There are four facets of quantum mechanics: states observables time evolution measurement.”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“The key feature is that the probability to tunnel through the barrier is exponentially suppressed. This is a general characteristic of tunnelling phenomena”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“We’re going to be interested in situations where the energy”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“This means”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“Rather than thinking of them as quantum probabilities for a single particle”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“The quantum novelty is that the wavefunction itself is not restricted only to the well: it leaks out into the surrounding region”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“the idea of parity”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“Solutions to the Schrödinger equation that behave as (2.85) are called bound states because they are necessarily trapped somewhere in the potential.”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“We learn that the Gaussian wavefunction (2.64) that we guessed earlier is actually the lowest energy state of the system”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“the energies are (2.73) All energies are proportional to”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“It’s difficult to overstate the importance of the harmonic oscillator in quantum mechanics. It is”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“Gaussian wavepacket. Clearly it describes a state that is fairly well localised in space. But”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“The discreteness in quantities like momentum and energy is one of the characteristic features of quantum mechanics. However”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics

“This is our first sign of the quantum in quantum mechanics. This word refers to the fact that certain quantities”
― David Tong, Quantum Mechanics: Volume 3: Lectures on Theoretical Physics