Uncertainty principle - Quiz
A) Earle Hesse Kennard B) Hermann Weyl C) Werner Heisenberg D) Max Planck
A) They are always independent. B) They can be known exactly at the same time. C) They can be measured with infinite precision. D) There is a limit to the precision with which certain pairs can be simultaneously known.
A) Inequalities B) Differential equations C) Equations D) Algebraic expressions
A) Independent variables B) Dependent variables C) Discrete variables D) Complementary variables
A) They are inversely proportional. B) They are Fourier transforms of one another. C) They are unrelated. D) They are identical.
A) ℏ = h B) ℏ = h * 2π C) ℏ = h / (2π) D) ℏ = h / π
A) The precision of the other property increases. B) The precision of the other property becomes infinite. C) The precision of the other property remains unchanged. D) The precision of the other property decreases.
A) It is unrelated to the uncertainty principle. B) It represents the exact limit of the uncertainty principle. C) It is a variable that can be adjusted. D) It is a theoretical concept with no practical application.
A) Summation B) Integration by parts C) Substitution D) Differentiation
A) It claims that variances are equal. B) It asserts that variances are always zero. C) It states that variances are independent. D) It provides a lower bound for the product of variances.
A) iℏ d/dx B) -iℏ d/dx C) -ℏ d/dx D) ℏ d/dx
A) It is used to calculate the variance. B) It is used to simplify the integration process. C) It is used to determine the mean value. D) It is used to define the wave function.
A) It remains constant. B) It becomes infinite. C) It oscillates. D) It vanishes.
A) They are independent. B) They are equal. C) They are directly proportional. D) They have an inverse relationship.
A) It interprets the wave function as a probability density amplitude. B) It states that the wave function is always zero. C) It defines the wave function as a constant. D) It describes the wave function as a deterministic function.
A) It measures the uncertainty. B) It defines the wave function. C) It calculates the variance. D) It relates position and momentum wavefunctions.
A) Variables that are unrelated. B) Variables that are independent of each other. C) Pairs of variables like position and momentum that are Fourier transforms of each other. D) Variables that are always equal.
A) It defines the wave function. B) It quantifies the precision of position and momentum. C) It calculates the variance. D) It measures the mean value.
A) Their product is unbounded. B) Their product is equal to ℏ. C) Their product is equal to zero. D) Their product is bounded from below by ℏ/2.
A) It defines the wave function. B) It measures the uncertainty. C) It calculates the variance. D) It is used to relate the position and momentum wavefunctions.
A) It defines the wave function. B) It measures the uncertainty. C) It is used to define the inner product in function space. D) It calculates the variance.
A) It measures the uncertainty. B) It defines the wave function. C) It relates the variances of position and momentum. D) It calculates the variance.
A) Self-adjoint operators B) Unitary operators C) Hermitian matrices D) Projection operators
A) Â + B̂ B) B̂Â - ÂB̂ C) ÂB̂ - B̂Â D) ÂB̂ + B̂Â
A) [x̂, p̂] = -iℏ B) [x̂, p̂] = ℏ C) [x̂, p̂] = iℏ D) [x̂, p̂] = 0
A) σx = ⟨x̂⟩² - ⟨x̂²⟩ B) σx = ⟨x̂²⟩ + ⟨x̂⟩² C) σx = ⟨x̂⟩ - ⟨x̂²⟩ D) σx = √⟨x̂²⟩ - ⟨x̂⟩²
A) σp = ⟨p̂²⟩ + ⟨p̂⟩² B) σp = ⟨p̂⟩ - ⟨p̂²⟩ C) σp = √⟨p̂²⟩ - ⟨p̂⟩² D) σp = ⟨p̂⟩² - ⟨p̂²⟩
A) Ô B) P̂ C) Û D) Î
A) a|n⟩ = |n-1⟩ B) a|n⟩ = sqrt(n)|n⟩ C) a|n⟩ = sqrt(n+1)|n-1⟩ D) a|n⟩ = sqrt(n)|n-1⟩
A) First excited state n=1 B) Ground state n=0 C) Second excited state n=2 D) Any state n
A) Exponential distribution B) Binomial distribution C) Normal distribution D) Uniform distribution
A) When Ω ≠ ω B) When x0 = 0 C) When ω = 0 D) When Ω = ω
A) Heisenberg B) Robertson C) Kennard D) Schrödinger
A) δ B) Δ C) μ D) σ
A) Kennard B) Schrödinger C) Heisenberg D) Robertson
A) The inverse operator B) The imaginary unit C) The integral operator D) The identity operator
A) Dennis Gabor B) Werner Heisenberg C) Carl Benedicks D) Albert Einstein
A) Square-shaped pulse B) Gaussian-shaped pulse C) Triangular-shaped pulse D) Sine-shaped pulse
A) Terence Tao. B) Niels Bohr. C) Richard Feynman. D) Albert Einstein.
A) ‖f‖L2(Rd) ≤ CeC(|S||Σ|)1/d (‖f‖L2(Sc) + ‖ƒ̂‖L2(Σc)). B) ‖f‖L2(Rd) = CeC|S||Σ| (‖f‖L2(Sc) + ‖ƒ̂‖L2(Σc)). C) ‖f‖L2(Rd) ≤ CeC|S||Σ| (‖f‖L2(Sc) + ‖ƒ̂‖L2(Σc)). D) ‖f‖L2(Rd) ≥ CeC|S||Σ| (‖f‖L2(Sc) + ‖ƒ̂‖L2(Σc)).
A) 1929 B) 1926 C) 1925 D) 1927
A) University of Copenhagen B) University of Göttingen C) University of Chicago D) Bohr's institute
A) Wolfgang Pauli B) Pascual Jordan C) Max Born D) Niels Bohr
A) 1927 B) 1925 C) 1929 D) 1930
A) 1927 B) 1925 C) 1930 D) 1929
A) Robertson B) Bohr C) Kennard D) Heisenberg
A) 1929 B) 1925 C) 1930 D) 1927
A) ħ B) σ C) h D) π
A) A telescope B) A spectrometer C) A microscope D) A particle accelerator
A) Bohr's critique B) Jordan's critique C) Born's critique D) Pauli's critique
A) Uncertainty B) Inaccuracy C) Indefiniteness D) Imprecision
A) Indefiniteness B) Inaccuracy C) Uncertainty D) Imprecision
A) The Planck constant B) The speed of light C) The gravitational constant D) The Boltzmann constant
A) The conservation of momentum B) The radically new noncommutativity C) The commutativity of quantum mechanics D) The accuracy of measurements
A) Spectroscopy, including particle physics. B) Classical mechanics. C) Electromagnetism. D) Thermodynamics.
A) 6×10-16 cm. B) 6×10-22 cm. C) 6×10-20 cm. D) 6×10-18 cm. |
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