When counting particle-in-a-box quantum states in three dimensions, why do we divide the "volume" of only one eighth of a full spherical shell by the "volume" per quantum state? Why not the full shell's volume?
A) Molecules in a gas can only have positive momentum components.
B) A single quantum energy state embraces both positive and negative values for each momentum component.
C) A particle's momentum magnitude must be positive.
D) The factor of 2 in the expression $h / 2 L$ already counts both possible momentum signs.
E) We really do include the full shell: the diagram only shows $1 / 8$ of the shell to make it easier to draw.
F) Some other reason (specify).

Question

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The Answer of When counting particle-in-a-box quantum states in three dimensions, why do we divide the "volume" of only one eighth of a full spherical shell by the "volume" per quantum state? Why not the full shell's volume?
A) Molecules in a gas can only have positive momentum components.
B) A single quantum energy state embraces both positive and negative values for each momentum component.
C) A particle's momentum magnitude must be positive.
D) The factor of 2 in the expression $h / 2 L$ already counts both possible momentum signs.
E) We really do include the full shell: the diagram only shows $1 / 8$ of the shell to make it easier to draw.
F) Some other reason (specify).

When Counting Particle-In-A-Box Quantum States in Three Dimensions, Why Do h/2Lh / 2 Lh/2L

When Counting Particle-In-A-Box Quantum States in Three Dimensions, Why Do $h / 2 L$