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