Exam 5: Matter Behaves Like Waves Quantum Physics

Suppose we put 20 non-interacting quantons into a one-dimensional box of length $L$ . The quantons quickly settle into the lowest possible energy states available. Roughly how many times larger will the quantons' total energy be if they are fermions as opposed to bosons? (Choose the closest answer.)

(Multiple Choice)

4.9/5

(47)

Question 101

Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. The inner product of a vector with itself $\langle u \mid u\rangle$ is a real number.

(True/False)

4.7/5

(47)

Question 102

In chapter Q1, we noted that the speed of sound in air depends on the air's temperature (increasing as the square root of the air temperature). Suppose a flute player tunes a flute that has been sitting in a cold automobile. As the flute warms up to room temperature, does it go sharp (A) or flat (B)?

(Multiple Choice)

4.8/5

(39)

Question 103

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

(True/False)

4.7/5

(37)

Question 104

As one approaches the bottom of a body of water, the circles shown in figure Q1.3 for water waves moving along the water's surface become increasingly vertically flattened ellipses. This means that the waves near the body's bottom are more (A) transverse or (B) longitudinal than those near the surface?

(Multiple Choice)

4.9/5

(35)

Question 105

Figure Q6.15 below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

(Multiple Choice)

4.8/5

(37)

Question 106

A hydrochloric acid molecule consists of a lightweight hydrogen atom bound to a much more massive chlorine atom. The interaction between the atoms is not purely attractive, but has a potential energy function that has a valley whose bottom corresponds to a certain nonzero distance between the atoms. If we ignore rotations, which of the idealized models in this chapter might best describe this molecule?

(Multiple Choice)

4.8/5

(35)

Question 107

Consider the experimental evidence we have discussed in the past few chapters. Classify the following experimental results according to the following scheme: For the quantons in question, the results: -A rapidly moving electron leaves a track in a bubble chamber photograph.

(Short Answer)

4.8/5

(33)

Question 108

Suppose that a quanton's energy is zero, irrespective of its spin orientation. Suppose further that we prepare this quanton in an arbitrary spin state $|\psi(0)\rangle$ . The probability of any possible experimental outcome for any spin observable will then be independent of time.

(True/False)

4.9/5

(38)

Question 109

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

(True/False)

4.7/5

(41)

Question 110

Exposure to radiation of any kind for long enough will tend to make an object radioactive.

(True/False)

4.8/5

(33)

Question 111

The point toward which compasses on the earth's surface point is a magnetic south pole.

(True/False)

4.8/5

(36)

Question 112

How many terms will appear in the square bracket of the simple harmonic oscillator eigenfunction if $n=7$ ?

(Multiple Choice)

4.9/5

(43)

Question 113

A quanton is moving in a classically allowed region. If the quanton would classically have at point $x_{A}$ twice the kinetic energy it would have at point $x_{B}$ , how would the wavelengths of an energy eigen function of the quanton compare at these points?

(Multiple Choice)

4.9/5

(42)

Question 114

Suppose that at a certain time a quanton has the (unrealistic) wave function shown below. $Suppose that at a certain time a quanton has the (unrealistic) wave function shown below. If we were to perform an experiment to locate the quanton, what is the probability that the result will be \geq 1 \mathrm{~nm} ? (Assume that \psi(x)=0 at all points outside the picture.)$ If we were to perform an experiment to locate the quanton, what is the probability that the result will be $\geq 1 \mathrm{~nm}$ ? (Assume that $\psi(x)=0$ at all points outside the picture.)

(Multiple Choice)

4.8/5

(34)

Question 115

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

(True/False)

4.7/5

(31)

Question 116

A meson is a subatomic "particle" consisting of a quark-antiquark pair. Suppose we have a meson consisting of an up quark and a much more massive bottom antiquark. The interaction between these point-like quarks is purely attractive, like that between oppositely charged particles. Which of the idealized models in this chapter might best describe this system's possible energy values?

(Multiple Choice)

4.8/5

(42)

Question 117

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ )except it is 207 times as massive. The classical model of spin would imply that a muon rotates

(Multiple Choice)

4.8/5

(32)

Question 118

If a complex number is equal to its own complex conjugate, then the complex number is real.

(True/False)

4.9/5

(37)

Question 119

Ignoring spin, the possible energies of a quanton moving in one dimension are only quantized if the quanton is bound.

(True/False)

4.9/5

(30)

Question 120

Showing 101 - 120 of 210

Suppose we put 20 non-interacting quantons into a one-dimensional box of length $L$ . The quantons quickly settle into the lowest possible energy states available. Roughly how many times larger will the quantons' total energy be if they are fermions as opposed to bosons? (Choose the closest answer.)

Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. The inner product of a vector with itself $\langle u \mid u\rangle$ is a real number.

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

Figure Q6.15 below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Consider the experimental evidence we have discussed in the past few chapters. Classify the following experimental results according to the following scheme: For the quantons in question, the results: -A rapidly moving electron leaves a track in a bubble chamber photograph.

Suppose that a quanton's energy is zero, irrespective of its spin orientation. Suppose further that we prepare this quanton in an arbitrary spin state $|\psi(0)\rangle$ . The probability of any possible experimental outcome for any spin observable will then be independent of time.

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

Exposure to radiation of any kind for long enough will tend to make an object radioactive.

The point toward which compasses on the earth's surface point is a magnetic south pole.

How many terms will appear in the square bracket of the simple harmonic oscillator eigenfunction if $n=7$ ?

A quanton is moving in a classically allowed region. If the quanton would classically have at point $x_{A}$ twice the kinetic energy it would have at point $x_{B}$ , how would the wavelengths of an energy eigen function of the quanton compare at these points?

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ )except it is 207 times as massive. The classical model of spin would imply that a muon rotates

If a complex number is equal to its own complex conjugate, then the complex number is real.

Ignoring spin, the possible energies of a quanton moving in one dimension are only quantized if the quanton is bound.

Conservation Laws Constrain Interactions

The Laws of Physics Are Universal Newtonian Mechanics

The Laws of Physics Are Frame-Independent Relativity

Electricity and Magnetism Are Unified

Some Processes Are Irreversible Thermal Physics

Filters

Exam 5: Matter Behaves Like Waves Quantum Physics

Consider two qqq -vectors ∣u⟩|u\rangle∣u⟩ and ∣w⟩|w\rangle∣w⟩ with possibly complex components. The inner product of a vector with itself ⟨u∣u⟩\langle u \mid u\rangle⟨u∣u⟩ is a real number.

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

Figure Q6.15 below shows a sequence of Stern-Gerlach devices. By analogy to the cases discussed in the chapter, what do you think are the probabilities that an electron entering the last device will come out of that device's plus and minus channels, respectively?

Consider the experimental evidence we have discussed in the past few chapters. Classify the following experimental results according to the following scheme: For the quantons in question, the results: -A rapidly moving electron leaves a track in a bubble chamber photograph.

Equation ∣v⃗∣=ωk=λT=λf|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f∣v∣=kω​=Tλ​=λf implies that a sinusoidal wave's phase speed depends on its wavelength.

Exposure to radiation of any kind for long enough will tend to make an object radioactive.

The point toward which compasses on the earth's surface point is a magnetic south pole.

How many terms will appear in the square bracket of the simple harmonic oscillator eigenfunction if n=7n=7n=7 ?

A quanton is moving in a classically allowed region. If the quanton would classically have at point xAx_{A}xA​ twice the kinetic energy it would have at point xBx_{B}xB​ , how would the wavelengths of an energy eigen function of the quanton compare at these points?

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

A muon is exactly like an electron (including having ∣s⃗∣=12ℏ|\vec{s}|=\frac{1}{2} \hbar∣s∣=21​ℏ )except it is 207 times as massive. The classical model of spin would imply that a muon rotates

If a complex number is equal to its own complex conjugate, then the complex number is real.

Ignoring spin, the possible energies of a quanton moving in one dimension are only quantized if the quanton is bound.

Conservation Laws Constrain Interactions

The Laws of Physics Are Universal Newtonian Mechanics

The Laws of Physics Are Frame-Independent Relativity

Electricity and Magnetism Are Unified

Some Processes Are Irreversible Thermal Physics

Filters

Consider two $q$ -vectors $|u\rangle$ and $|w\rangle$ with possibly complex components. The inner product of a vector with itself $\langle u \mid u\rangle$ is a real number.

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

How many terms will appear in the square bracket of the simple harmonic oscillator eigenfunction if $n=7$ ?

A quanton is moving in a classically allowed region. If the quanton would classically have at point $x_{A}$ twice the kinetic energy it would have at point $x_{B}$ , how would the wavelengths of an energy eigen function of the quanton compare at these points?

A muon is exactly like an electron (including having $|\vec{s}|=\frac{1}{2} \hbar$ )except it is 207 times as massive. The classical model of spin would imply that a muon rotates